هندسة جبرية

This Togliatti surface is an algebraic surface of degree five. The picture represents a portion of its real locus.

الهندسة الجبرية Algebraic geometry هي أحد فروع الرياضيات التي تدمج الجبر التجريدي خصوصا الجبر التبديلي مع الهندسة .

يمكن حتى نراه على أنه مجموعات حلول solution set لجمل المعادلات الجبرية. عندما لاقد يكون هناك أكثر من متغير واحد تدخل الاعتبارات الهنسية في الموضوع كثيرا لفهم الظاهرة المدروسة.

Basic notions

Zeros of simultaneous polynomials

Sphere and slanted circle

تنويعة إسقاطية

Parabola (y = x², red) and cubic (y = x³, blue) in projective space

انظر أيضاً

فهم الإحصاء الجبري
Differential geometry
Geometric algebra
Glossary of classical algebraic geometry
Intersection theory
Important publications in algebraic geometry
List of algebraic surfaces
Noncommutative algebraic geometry
Differential algebraic geometry
Real algebraic geometry

الهامش

للاستزادة

Some classic textbooks that predate schemes

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 . Zbl 0796.14001.
Hodge, W. V. D.; Pedoe, Daniel (1994). Methods of Algebraic Geometry Volume 2. Cambridge University Press. ISBN . Zbl 0796.14002.
Hodge, W. V. D.; Pedoe, Daniel (1994). Methods of Algebraic Geometry Volume 3. Cambridge University Press. ISBN . Zbl 0796.14003.

Modern textbooks that do not use the language of schemes

Garrity, Thomas; et al. (2013). Algebraic Geometry A Problem Solving Approach. American Mathematical Society. ISBN .
Griffiths, Phillip; Harris, Joe (1994). Principles of Algebraic Geometry. Wiley-Interscience. ISBN . Zbl 0836.14001.
Harris, Joe (1995). Algebraic Geometry A First Course. Springer-Verlag. ISBN . Zbl 0779.14001.
Mumford, David (1995). Algebraic Geometry I Complex Projective Varieties (2nd ed.). Springer-Verlag. ISBN . Zbl 0821.14001.
Reid, Miles (1988). Undergraduate Algebraic Geometry. Cambridge University Press. ISBN . Zbl 0701.14001.
Shafarevich, Igor (1995). Basic Algebraic Geometry I Varieties in Projective Space (2nd ed.). Springer-Verlag. ISBN . Zbl 0797.14001.

Textbooks in computational algebraic geometry

Cox, David A.; Little, John; O'Shea, Donal (1997). Ideals, Varieties, and Algorithms (2nd ed.). Springer-Verlag. ISBN . Zbl 0861.13012.
Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise (2006). . Springer-Verlag.
González-Vega, Laureano; Recio, Tómas (1996). Algorithms in algebraic geometry and applications. Birkhaüser.
Elkadi, Mohamed; Mourrain, Bernard; Piene, Ragni, eds. (2006). Algebraic geometry and geometric modeling. Springer-Verlag.
Dickenstein, Alicia; Schreyer, Frank-Olaf; Sommese, Andrew J., eds. (2008). Algorithms in Algebraic Geometry. The IMA Volumes in Mathematics and its Applications. 146. Springer. ISBN . 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.

Textbooks and references for schemes

Eisenbud, David; Harris, Joe (1998). The Geometry of Schemes. Springer-Verlag. ISBN . 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 ed.). Springer-Verlag. ISBN . Zbl 0203.23301.
Hartshorne, Robin (1977). Algebraic Geometry. Springer-Verlag. ISBN . Zbl 0367.14001.
Mumford, David (1999). The Red Book of Varieties and Schemes Includes the Michigan Lectures on Curves and Their Jacobians (2nd ed.). Springer-Verlag. ISBN . Zbl 0945.14001.
Shafarevich, Igor (1995). Basic Algebraic Geometry II Schemes and complex manifolds (2nd ed.). Springer-Verlag. ISBN . Zbl 0797.14002.

وصلات خارجية

by Ravi Vakil, 764 pp.
entry on PlanetMath
English translation of the van der Waerden textbook
The History of Algebraic Geometry (1.425 Gigabyte MOV file), a 1972 talk by Jean Dieudonné at the Department of Mathematics of the University of Wisconsin-Milwaukee
The Stacks Project, an open source textbook and reference work on algebraic stacks and algebraic geometry