Algebarska geometrija — разлика између измена

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Верзија на датум 20. новембар 2019. у 00:26

Algebarska geometrija je grana matematike koja kombinuje tehnike apstraktne algebre, posebno komutativne algebre, sa jezikom i problematikom geometrije. Ona ima važno mesto u današnjoj matematici i ima brojne konceptualne veze sa različitim poljima kao što su kompleksna analiza, topologija i teorija brojeva. Algebarska geometrija je grana matematike koja klasično studira zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the curve and relations between the curves given by different equations.

Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

In the 20th century, algebraic geometry split into several subareas.

The mainstream of algebraic geometry is devoted to the study of the complex points of the algebraic varieties and more generally to the points with coordinates in an algebraically closed field.
Real algebraic geometry is the study of the real points of an algebraic variety.
Diophantine geometry and, more generally, arithmetic geometry is the study of the points of an algebraic variety with coordinates in fields that are not algebraically closed and occur in algebraic number theory, such as the field of rational numbers, number fields, finite fields, function fields, and p-adic fields.
A large part of singularity theory is devoted to the singularities of algebraic varieties.
Computational algebraic geometry is an area that has emerged at the intersection of algebraic geometry and computer algebra, with the rise of computers. It consists mainly of algorithm design and software development for the study of properties of explicitly given algebraic varieties.

Much of the development of the mainstream of algebraic geometry in the 20th century occurred within an abstract algebraic framework, with increasing emphasis being placed on "intrinsic" properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space; this parallels developments in topology, differential and complex geometry. One key achievement of this abstract algebraic geometry is Grothendieck's scheme theory which allows one to use sheaf theory to study algebraic varieties in a way which is very similar to its use in the study of differential and analytic manifolds. This is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through Hilbert's Nullstellensatz, with a maximal ideal of the coordinate ring, while the points of the corresponding affine scheme are all prime ideals of this ring. This means that a point of such a scheme may be either a usual point or a subvariety. This approach also enables a unification of the language and the tools of classical algebraic geometry, mainly concerned with complex points, and of algebraic number theory. Wiles' proof of the longstanding conjecture called Fermat's last theorem is an example of the power of this approach.

Aplikacije

Algebarska geometrija now finds applications in statistics,^[1] control theory,^[2]^[3] robotics,^[4] error-correcting codes,^[5] phylogenetics^[6] and geometric modelling.^[7] There are also connections to string theory,^[8] game theory,^[9] graph matchings,^[10] solitons^[11] and integer programming.^[12]

Reference

^ Drton, Mathias; Sturmfels, Bernd; Sullivant, Seth (2009). Lectures on Algebraic Statistics. Springer. ISBN 978-3-7643-8904-8.
^ Falb, Peter (1990). Methods of Algebraic Geometry in Control Theory Part II Multivariable Linear Systems and Projective Algebraic Geometry. Springer. ISBN 978-0-8176-4113-9.
^ Allen Tannenbaum (1982), Invariance and Systems Theory: Algebraic and Geometric Aspects, Lecture Notes in Mathematics, volume 845, Springer-Verlag, ISBN 9783540105657
^ Selig, J.M. (2005). Geometric Fundamentals of Robotics. Springer. ISBN 978-0-387-20874-9.
^ Tsfasman, Michael A.; Vlăduț, Serge G.; Nogin, Dmitry (1990). Algebraic Geometric Codes Basic Notions. American Mathematical Soc. ISBN 978-0-8218-7520-9.
^ Barry Arthur Cipra (2007), Algebraic Geometers See Ideal Approach to Biology Архивирано 2016-03-03 на сајту Wayback Machine, SIAM News, Volume 40, Number 6
^ Jüttler, Bert; Piene, Ragni (2007). Geometric Modeling and Algebraic Geometry. Springer. ISBN 978-3-540-72185-7.
^ Cox, David A.; Katz, Sheldon (1999). Mirror Symmetry and Algebraic Geometry. American Mathematical Soc. ISBN 978-0-8218-2127-5.
^ Blume, L. E.; Zame, W. R. (1994). „The algebraic geometry of perfect and sequential equilibrium” (PDF). Econometrica. 62 (4): 783—794. JSTOR 2951732.
^ Kenyon, Richard; Okounkov, Andrei; Sheffield, Scott (2003). „Dimers and Amoebae”. arXiv:math-ph/0311005 .
^ Fordy, Allan P. (1990). Soliton Theory A Survey of Results. Manchester University Press. ISBN 978-0-7190-1491-8.
^ Cox, David A.; Sturmfels, Bernd. Manocha, Dinesh N., ур. Applications of Computational Algebraic Geometry. American Mathematical Soc. ISBN 978-0-8218-6758-7.

Literatura

van der Waerden, B. L. (1945). Einfuehrung in die algebraische Geometrie. Dover.
Hodge, W. V. D.; Pedoe, Daniel (1994). Methods of Algebraic Geometry Volume 1. Cambridge University Press. ISBN 978-0-521-46900-5. Zbl 0796.14001.
Hodge, W. V. D.; Pedoe, Daniel (1994). Methods of Algebraic Geometry Volume 2. Cambridge University Press. ISBN 978-0-521-46901-2. Zbl 0796.14002.
Hodge, W. V. D.; Pedoe, Daniel (1994). Methods of Algebraic Geometry Volume 3. Cambridge University Press. ISBN 978-0-521-46775-9. Zbl 0796.14003.
Garrity, Thomas; et al. (2013). Algebraic Geometry A Problem Solving Approach. American Mathematical Society. ISBN 978-0-821-89396-8.
Griffiths, Phillip; Harris, Joe (1994). Principles of Algebraic Geometry. Wiley-Interscience. ISBN 978-0-471-05059-9. Zbl 0836.14001.
Harris, Joe (1995). Algebraic Geometry A First Course. Springer-Verlag. ISBN 978-0-387-97716-4. Zbl 0779.14001.
Mumford, David (1995). Algebraic Geometry I Complex Projective Varieties (2nd изд.). Springer-Verlag. ISBN 978-3-540-58657-9. Zbl 0821.14001.
Reid, Miles (1988). Undergraduate Algebraic Geometry. Cambridge University Press. ISBN 978-0-521-35662-6. Zbl 0701.14001.
Shafarevich, Igor (1995). Basic Algebraic Geometry I Varieties in Projective Space (2nd изд.). Springer-Verlag. ISBN 978-0-387-54812-8. Zbl 0797.14001.
Cox, David A.; Little, John; O'Shea, Donal (1997). Ideals, Varieties, and Algorithms (2nd изд.). Springer-Verlag. ISBN 978-0-387-94680-1. Zbl 0861.13012.
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise (2006). Algorithms in real algebraic geometry. Springer-Verlag.
González-Vega, Laureano; Recio, Tómas (1996). Algorithms in algebraic geometry and applications. Birkhaüser.
Elkadi, Mohamed; Mourrain, Bernard; Piene, Ragni, ур. (2006). Algebraic geometry and geometric modeling. Springer-Verlag.
Dickenstein, Alicia; Schreyer, Frank-Olaf; Sommese, Andrew J., ур. (2008). Algorithms in Algebraic Geometry. The IMA Volumes in Mathematics and its Applications. 146. Springer. ISBN 9780387751559. LCCN 2007938208.
Cox, David A.; Little, John B.; O'Shea, Donal (1998). Using algebraic geometry. Springer-Verlag.
Caviness, Bob F.; Johnson, Jeremy R. (1998). Quantifier elimination and cylindrical algebraic decomposition. Springer-Verlag.
Eisenbud, David; Harris, Joe (1998). The Geometry of Schemes. Springer-Verlag. ISBN 978-0-387-98637-1. Zbl 0960.14002.
Grothendieck, Alexander (1960). Éléments de géométrie algébrique. Publications Mathématiques de l'IHÉS. Zbl 0118.36206.
Grothendieck, Alexander; Dieudonné, Jean Alexandre (1971). Éléments de géométrie algébrique. 1 (2nd изд.). Springer-Verlag. ISBN 978-3-540-05113-8. Zbl 0203.23301.
Hartshorne, Robin (1977). Algebraic Geometry. Springer-Verlag. ISBN 978-0-387-90244-9. Zbl 0367.14001.
Mumford, David (1999). The Red Book of Varieties and Schemes Includes the Michigan Lectures on Curves and Their Jacobians (2nd изд.). Springer-Verlag. ISBN 978-3-540-63293-1. Zbl 0945.14001.
Shafarevich, Igor (1995). Basic Algebraic Geometry II Schemes and complex manifolds (2nd изд.). Springer-Verlag. ISBN 978-3-540-57554-2. Zbl 0797.14002.

Spoljašnje veze

Foundations of Algebraic Geometry by Ravi Vakil, 808 pp.
Algebraic geometry entry on PlanetMath
English translation of the van der Waerden textbook
Dieudonné, Jean (3. 3. 1972). „The History of Algebraic Geometry”. Talk at the Department of Mathematics of the University of Wisconsin–Milwaukee — преко YouTube.
The Stacks Project, an open source textbook and reference work on algebraic stacks and algebraic geometry

[1] Drton, Mathias; Sturmfels, Bernd; Sullivant, Seth (2009). Lectures on Algebraic Statistics. Springer. ISBN 978-3-7643-8904-8.

[2] Falb, Peter (1990). Methods of Algebraic Geometry in Control Theory Part II Multivariable Linear Systems and Projective Algebraic Geometry. Springer. ISBN 978-0-8176-4113-9.

[3] Allen Tannenbaum (1982), Invariance and Systems Theory: Algebraic and Geometric Aspects, Lecture Notes in Mathematics, volume 845, Springer-Verlag, ISBN 9783540105657

[4] Selig, J.M. (2005). Geometric Fundamentals of Robotics. Springer. ISBN 978-0-387-20874-9.

[5] Tsfasman, Michael A.; Vlăduț, Serge G.; Nogin, Dmitry (1990). Algebraic Geometric Codes Basic Notions. American Mathematical Soc. ISBN 978-0-8218-7520-9.

[6] Barry Arthur Cipra (2007), Algebraic Geometers See Ideal Approach to Biology Архивирано 2016-03-03 на сајту Wayback Machine, SIAM News, Volume 40, Number 6

[7] Jüttler, Bert; Piene, Ragni (2007). Geometric Modeling and Algebraic Geometry. Springer. ISBN 978-3-540-72185-7.

[8] Cox, David A.; Katz, Sheldon (1999). Mirror Symmetry and Algebraic Geometry. American Mathematical Soc. ISBN 978-0-8218-2127-5.

[9] Blume, L. E.; Zame, W. R. (1994). „The algebraic geometry of perfect and sequential equilibrium” (PDF). Econometrica. 62 (4): 783—794. JSTOR 2951732.

[10] Kenyon, Richard; Okounkov, Andrei; Sheffield, Scott (2003). „Dimers and Amoebae”. arXiv:math-ph/0311005 .

[11] Fordy, Allan P. (1990). Soliton Theory A Survey of Results. Manchester University Press. ISBN 978-0-7190-1491-8.

[12] Cox, David A.; Sturmfels, Bernd. Manocha, Dinesh N., ур. Applications of Computational Algebraic Geometry. American Mathematical Soc. ISBN 978-0-8218-6758-7.

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@@ Ред 1: / Ред 1: @@
+{{short description|Grana matematike}}
-'''Алгебарска геометрија''' је грана [[математика|математике]] која, као што и име каже, комбинује технике [[апстрактна алгебра|апстрактне алгебре]], посебно [[комутативна алгебра|комутативне алгебре]],  са језиком и проблематиком [[геометрија|геометрије]]. Има важно место у данашњој математици и има бројне концептуалне везе са различитим пољима као што су [[комплексна анализа]], [[топологија]] и [[теорија бројева]].
+[[File:Togliatti surface.png|thumb|This [[Togliatti surface]] is an [[algebraic surface]] of degree five. The picture represents a portion of its real [[locus (mathematics)|locus]].]]
+{{rut}}
+'''Algebarska geometrija''' je grana [[matematika|matematike]] koja kombinuje tehnike [[apstraktna algebra|apstraktne algebre]], posebno [[komutativna algebra|komutativne algebre]], sa jezikom i problematikom [[geometrija|geometrije]]. Ona ima važno mesto u današnjoj matematici i ima brojne konceptualne veze sa različitim poljima kao što su [[kompleksna analiza]], [[topologija]] i [[teorija brojeva]]. Algebarska geometrija je grana matematike koja klasično studira [[zero of a function|zeros]] of [[multivariate polynomial]]s. Modern algebraic geometry is based on the use of [[Abstract algebra|abstract algebraic]] techniques, mainly from [[commutative algebra]], for solving  [[geometry|geometrical problems]] about these sets of zeros.
+The fundamental objects of study in algebraic geometry are [[algebraic variety|algebraic varieties]], which are geometric manifestations of [[solution set|solutions]] of [[systems of polynomial equations]]. Examples of the most studied classes of algebraic varieties are: [[plane algebraic curve]]s, which include [[line (geometry)|lines]], [[circle]]s, [[parabola]]s, [[ellipse]]s, [[hyperbola]]s, [[cubic curve]]s like [[elliptic curve]]s, and quartic curves like [[lemniscate of Bernoulli|lemniscate]]s and [[Cassini oval]]s. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given [[polynomial equation]]. Basic questions involve the study of the points of special interest like the [[singular point of a curve|singular point]]s, the [[inflection point]]s and the [[point at infinity|points at infinity]]. More advanced questions involve the [[topology]] of the curve and relations between the curves given by different equations.
-{{клица-математика}}
+Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as [[complex analysis]], [[topology]] and [[number theory]]. Initially a study of [[systems of polynomial equations]] in several variables, the subject of algebraic geometry starts where [[equation solving]] leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.
+In the 20th century, algebraic geometry split into several subareas.
+* The mainstream of algebraic geometry is devoted to the study of the complex points of the algebraic varieties and more generally to the points with coordinates in an [[algebraically closed field]].
+* [[Real algebraic geometry]] is the study of the real points of an algebraic variety.
+* [[Diophantine geometry]] and, more generally, [[arithmetic geometry]] is the study of the points of an algebraic variety with coordinates in [[field (mathematics)|field]]s that are not [[algebraically closed]] and occur in [[algebraic number theory]], such as the field of [[rational number]]s, [[number field]]s, [[finite field]]s, [[Algebraic function field|function fields]], and [[p-adic number|''p''-adic field]]s.
+* A large part of [[Singularity theory#Singularities in algebraic geometry|singularity theory]] is devoted to the singularities of algebraic varieties.
+* [[#Computational algebraic geometry|Computational algebraic geometry]] is an area that has emerged at the intersection of algebraic geometry and [[computer algebra]], with the rise of computers. It consists mainly of [[algorithm]] design and [[software]] development for the study of properties of explicitly given algebraic varieties.
+Much of the development of the mainstream of algebraic geometry in the 20th century occurred within an abstract algebraic framework, with increasing emphasis being placed on "intrinsic" properties of algebraic varieties not dependent on any particular way of embedding the variety in an ambient coordinate space; this parallels developments in [[topology]], [[differential geometry|differential]] and [[complex geometry]]. One key achievement of this abstract algebraic geometry is [[Grothendieck]]'s [[scheme theory]] which allows one to use [[sheaf theory]] to study algebraic varieties in a way which is very similar to its use in the study of [[differential manifold|differential]] and [[complex manifold|analytic manifolds]]. This is obtained by extending the notion of point: In classical algebraic geometry, a point of an affine variety may be identified, through [[Hilbert's Nullstellensatz]], with a [[maximal ideal]] of the [[coordinate ring]], while the points of the corresponding affine scheme are all prime ideals of this ring. This means that a point of such a scheme may be either a usual point or a subvariety. This approach also enables a unification of the language and the tools of classical algebraic geometry, mainly concerned with complex points, and of algebraic number theory. [[Wiles's proof of Fermat's Last Theorem|Wiles' proof]] of the longstanding conjecture called [[Fermat's last theorem]] is an example of the power of this approach.
+== Aplikacije ==
+Algebarska geometrija now finds applications in [[algebraic statistics|statistics]],<ref>{{cite book| last1 = Drton| first1 = Mathias| last2 = Sturmfels| first2 = Bernd| last3 = Sullivant| first3 = Seth| title = Lectures on Algebraic Statistics| url = https://books.google.com/?id=TytYUTy5V_IC| year = 2009| publisher = Springer| isbn = 978-3-7643-8904-8 }}</ref> [[control theory]],<ref>{{cite book| last = Falb| first = Peter| title = Methods of Algebraic Geometry in Control Theory Part II Multivariable Linear Systems and Projective Algebraic Geometry| url = https://books.google.com/?id=V--84aGmWh4C| year = 1990| publisher = Springer| isbn = 978-0-8176-4113-9 }}</ref><ref>[[Allen Tannenbaum]] (1982), Invariance and Systems Theory: Algebraic and Geometric Aspects, Lecture Notes in Mathematics, volume 845, Springer-Verlag, {{ISBN|9783540105657}}</ref> [[robotics]],<ref>{{cite book| last = Selig| first = J.M.| title = Geometric Fundamentals of Robotics| url = https://books.google.com/?id=9FljXoISr8AC| year = 2005| publisher = Springer| isbn = 978-0-387-20874-9 }}</ref> [[algebraic geometric code|error-correcting codes]],<ref>{{cite book |last1=Tsfasman |first1=Michael A. |last2=Vlăduț |first2=Serge G. |last3=Nogin |first3=Dmitry |title=Algebraic Geometric Codes Basic Notions |year=1990 |publisher=American Mathematical Soc. |isbn=978-0-8218-7520-9 |url=https://books.google.com/?id=o2sA-wzDBLkC}}</ref> [[computational phylogenetics|phylogenetics]]<ref>[[Barry Arthur Cipra]] (2007), [http://siam.org/pdf/news/1146.pdf Algebraic Geometers See Ideal Approach to Biology] {{Webarchive|url=https://web.archive.org/web/20160303230428/http://siam.org/pdf/news/1146.pdf# |date=2016-03-03 }}, SIAM News, Volume 40, Number 6</ref> and [[geometric modelling]].<ref>{{cite book |last1=Jüttler |first1=Bert |last2=Piene |first2=Ragni |title=Geometric Modeling and Algebraic Geometry |year=2007 |publisher=Springer |isbn=978-3-540-72185-7 |url=https://books.google.com/?id=1wNGq87gWykC}}</ref> There are also connections to [[Homological mirror symmetry|string theory]],<ref>{{cite book |last1=Cox |first1=David A. |authorlink1=David A. Cox |last2=Katz |first2=Sheldon |title=Mirror Symmetry and Algebraic Geometry |url=https://books.google.com/?id=Z8u3ngEACAAJ |year=1999 |publisher=American Mathematical Soc. |isbn=978-0-8218-2127-5}}</ref> [[game theory]],<ref>{{cite journal |url=https://pdfs.semanticscholar.org/dffa/971f61a74202b3b30df905cefed29a95d201.pdf |title=The algebraic geometry of perfect and sequential equilibrium |first=L. E. |last=Blume |first2=W. R. |last2=Zame |journal=[[Econometrica]] |volume=62 |issue=4 |year=1994 |pages=783–794 |jstor=2951732 }}</ref> [[Matching (graph theory)|graph matching]]s,<ref>{{cite arXiv |last1=Kenyon |first1=Richard |last2=Okounkov |first2=Andrei |last3=Sheffield |first3=Scott |title=Dimers and Amoebae |eprint=math-ph/0311005 |year=2003}}</ref> [[soliton]]s<ref>{{cite book |last=Fordy |first=Allan P. |title=Soliton Theory A Survey of Results |url=https://books.google.com/?id=eO_PAAAAIAAJ |year=1990 |publisher=Manchester University Press |isbn=978-0-7190-1491-8}}</ref> and [[integer programming]].<ref>{{cite book |last1=Cox |first1=David A. |authorlink1=David A. Cox |last2=Sturmfels |first2=Bernd |editor-last=Manocha |editor-first=Dinesh N. |title=Applications of Computational Algebraic Geometry |url=https://books.google.com/?id=fe0MJEPDwzAC |publisher=American Mathematical Soc. |isbn=978-0-8218-6758-7}}</ref>
+== Reference ==
+{{Reflist|}}
+== Literatura ==
+{{Refbegin|30em}}
+* {{cite book
+ |last=van der Waerden |first=B. L. |authorlink=B. L. van der Waerden
+ |year = 1945
+ |title = Einfuehrung in die algebraische Geometrie
+ |publisher = [[Dover]]
+}}
+* {{cite book |last1=Hodge |first1=W. V. D. |authorlink1=W. V. D. Hodge |last2=Pedoe |first2=Daniel |authorlink2=Daniel Pedoe |title=Methods of Algebraic Geometry Volume 1 |year=1994 |publisher=[[Cambridge University Press]] |isbn=978-0-521-46900-5 |zbl=0796.14001}}
+* {{cite book| last1 = Hodge| first1 = W. V. D.| authorlink1 = W. V. D. Hodge| last2 = Pedoe| first2 = Daniel| authorlink2 = Daniel Pedoe| title = Methods of Algebraic Geometry Volume 2| year = 1994| publisher = [[Cambridge University Press]]| isbn = 978-0-521-46901-2| zbl = 0796.14002 }}
+* {{cite book| last1 = Hodge| first1 = W. V. D.| authorlink1 = W. V. D. Hodge| last2 = Pedoe| first2 = Daniel| authorlink2 = Daniel Pedoe| title = Methods of Algebraic Geometry Volume 3| year = 1994| publisher = [[Cambridge University Press]]| isbn = 978-0-521-46775-9| zbl = 0796.14003 }}
+* {{cite book| last = Garrity| first = Thomas| title = Algebraic Geometry A Problem Solving Approach| year = 2013| publisher = [[American Mathematical Society]]| isbn = 978-0-821-89396-8|display-authors=etal}}
+* {{cite book
+ | last1=Griffiths | first1=Phillip | authorlink1=Phillip Griffiths
+ | last2=Harris | first2=Joe | authorlink2=Joe Harris (mathematician)
+ | year = 1994
+ | title = Principles of Algebraic Geometry
+ | publisher = [[Wiley-Interscience]]
+ | isbn = 978-0-471-05059-9
+ | zbl = 0836.14001
+}}
+* {{cite book| last = Harris| first = Joe| authorlink = Joe Harris (mathematician)| title = Algebraic Geometry A First Course| year = 1995| publisher = [[Springer Science+Business Media|Springer-Verlag]]| isbn = 978-0-387-97716-4| zbl = 0779.14001 }}
+* {{cite book| last = Mumford| first = David| authorlink = David Mumford| title = Algebraic Geometry I Complex Projective Varieties| edition = 2nd| year = 1995| publisher = [[Springer Science+Business Media|Springer-Verlag]]| isbn = 978-3-540-58657-9| zbl = 0821.14001 }}
+* {{cite book| last = Reid| first = Miles| authorlink = Miles Reid| title = Undergraduate Algebraic Geometry| url = https://archive.org/details/undergraduatealg0000reid| url-access = registration| year = 1988| publisher = [[Cambridge University Press]]| isbn = 978-0-521-35662-6| zbl = 0701.14001 }}
+* {{cite book| last = Shafarevich| first = Igor| authorlink = Igor Shafarevich| title = Basic Algebraic Geometry I Varieties in Projective Space| edition = 2nd| year = 1995| publisher = [[Springer Science+Business Media|Springer-Verlag]]| isbn = 978-0-387-54812-8| zbl = 0797.14001 }}
+* {{cite book |last1=Cox |first1=David A. |authorlink1=David A. Cox |last2=Little |first2=John |last3=O'Shea |first3=Donal |title=Ideals, Varieties, and Algorithms |edition=2nd |year=1997 |publisher=[[Springer Science+Business Media|Springer-Verlag]] |isbn=978-0-387-94680-1 |zbl=0861.13012}}
+* {{cite book
+ | last1=Basu |first1 = Saugata
+ | last2=Pollack |first2=Richard
+ | last3=Roy |first3=Marie-Françoise
+ | year = 2006
+ | title = Algorithms in real algebraic geometry
+ | publisher = [[Springer Science+Business Media|Springer-Verlag]]
+ | url = http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-ed2-posted1.html
+}}
+* {{cite book
+ | last1=González-Vega |first1=Laureano
+ | last2=Recio |first2=Tómas
+ | year = 1996
+ | title = Algorithms in algebraic geometry and applications
+ | publisher = Birkhaüser
+}}
+* {{cite book
+ | editor1-last=Elkadi |editor1-first=Mohamed
+ | editor2-last=Mourrain |editor2-first=Bernard
+ | editor3-last=Piene |editor3-first=Ragni
+ | year = 2006
+ | title = Algebraic geometry and geometric modeling
+ | publisher = [[Springer Science+Business Media|Springer-Verlag]]
+}}
+* {{cite book
+ | editor1-last=Dickenstein |editor1-first=Alicia|editor1-link=Alicia Dickenstein
+ | editor2-last=Schreyer |editor2-first=Frank-Olaf
+ | editor3-last=Sommese |editor3-first=Andrew J.
+ | year = 2008
+ | title = Algorithms in Algebraic Geometry
+ | volume=146
+ | series=The IMA Volumes in Mathematics and its Applications
+ | publisher = [[Springer Science+Business Media|Springer]]
+ | isbn=9780387751559
+ | lccn=2007938208
+}}
+* {{cite book
+ | last1=Cox |first1=David A. |authorlink1=David A. Cox
+ | last2=Little |first2=John B.
+ | last3=O'Shea |first3=Donal
+ | year = 1998
+ | title = Using algebraic geometry
+ | url=https://archive.org/details/springer_10.1007-978-1-4757-6911-1 | publisher = [[Springer Science+Business Media|Springer-Verlag]]
+}}
+* {{cite book
+ | last1=Caviness |first1=Bob F.
+ | last2=Johnson |first2=Jeremy R.
+ | year = 1998
+ | title = Quantifier elimination and cylindrical algebraic decomposition
+ | publisher = [[Springer Science+Business Media|Springer-Verlag]]
+}}
+* {{cite book |last1=Eisenbud |first1=David |authorlink1=David Eisenbud |last2=Harris |first2=Joe |authorlink2=Joe Harris (mathematician) |title=The Geometry of Schemes |url=https://archive.org/details/springer_10.1007-978-0-387-22639-2 |year=1998 |publisher=[[Springer Science+Business Media|Springer-Verlag]] |isbn=978-0-387-98637-1 |zbl=0960.14002}}
+* {{cite book
+ | last=Grothendieck |first=Alexander |authorlink=Alexander Grothendieck
+ | year = 1960
+ | title = Éléments de géométrie algébrique
+ | publisher = [[Publications Mathématiques de l'IHÉS]]
+ | zbl = 0118.36206
+|title-link=Éléments de géométrie algébrique }}
+* {{cite book |last1=Grothendieck |first1=Alexander |authorlink1=Alexander Grothendieck |last2=Dieudonné |first2=Jean Alexandre |title=Éléments de géométrie algébrique |edition=2nd |volume=1 |year=1971 |publisher=[[Springer Science+Business Media|Springer-Verlag]] |isbn=978-3-540-05113-8 |zbl=0203.23301|title-link=Éléments de géométrie algébrique }}
+* {{cite book |last=Hartshorne |first=Robin |authorlink=Robin Hartshorne |title=Algebraic Geometry |year=1977 |publisher=[[Springer Science+Business Media|Springer-Verlag]] |isbn=978-0-387-90244-9 |zbl=0367.14001|title-link=Algebraic Geometry (book) }}
+* {{cite book |last=Mumford |first=David |authorlink=David Mumford |title=The Red Book of Varieties and Schemes Includes the Michigan Lectures on Curves and Their Jacobians |edition=2nd |year=1999 |publisher=[[Springer Science+Business Media|Springer-Verlag]] |isbn=978-3-540-63293-1 |zbl=0945.14001}}
+* {{cite book| last = Shafarevich| first = Igor| authorlink = Igor Shafarevich| title = Basic Algebraic Geometry II Schemes and complex manifolds| edition = 2nd| year = 1995| publisher = [[Springer Science+Business Media|Springer-Verlag]]| isbn = 978-3-540-57554-2| zbl = 0797.14002| url-access = registration| url = https://archive.org/details/basicalgebraicge00irsh}}
+{{refend}}
+== Spoljašnje veze ==
+{{Commons category-lat|Algebraic geometry}}
+* -{[http://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf ''Foundations of Algebraic Geometry'' by Ravi Vakil, 808 pp.]}-
+* -{[https://web.archive.org/web/20040415021548/http://planetmath.org/encyclopedia/AlgebraicGeometry.html ''Algebraic geometry''] entry on [http://planetmath.org/ PlanetMath]}-
+* -{[http://neo-classical-physics.info/uploads/3/0/6/5/3065888/van_der_waerden_-_algebraic_geometry.pdf English translation of the van der Waerden textbook]}-
+* {{cite web |first=Jean |last=Dieudonné |authorlink=Jean Dieudonné |date=March 3, 1972 |title=The History of Algebraic Geometry |url=https://www.youtube.com/watch?v=Jzx-0poj3Eo |publisher=Talk at the Department of Mathematics of the [[University of Wisconsin–Milwaukee]] |via=[[YouTube]] }}
+* -{[http://stacks.math.columbia.edu/ The Stacks Project], an open source textbook and reference work on algebraic stacks and algebraic geometry}-
+{{Oblasti matematike-lat| state=collapsed}}
+{{Authority control-lat}}
+{{DEFAULTSORT:Алгебарска геометрија}}
 [[Категорија:Алгебарска геометрија|*]]

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