هندسة جبرية
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الهندسة الجبرية Algebraic geometry هي أحد فروع الرياضيات التي تدمج الجبر التجريدي خصوصا الجبر التبديلي مع الهندسة .
يمكن أن نراه على أنه مجموعات حلول solution set لجمل المعادلات الجبرية. عندما لا يكون هناك أكثر من متغير واحد تدخل الاعتبارات الهنسية في الموضوع كثيرا لفهم الظاهرة المدروسة.
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المفاهيم الأساسية
أصفار عديدات الحدود الآنية
تنويعة إسقاطية
انظر أيضاً
- علم 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 0-521-46900-7. Zbl 0796.14001.
- Hodge, W. V. D.; Pedoe, Daniel (1994). Methods of Algebraic Geometry Volume 2. Cambridge University Press. ISBN 0-521-46901-5. Zbl 0796.14002.
- Hodge, W. V. D.; Pedoe, Daniel (1994). Methods of Algebraic Geometry Volume 3. Cambridge University Press. ISBN 0-521-46775-6. 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 0-821-89396-3.
- Griffiths, Phillip; Harris, Joe (1994). Principles of Algebraic Geometry. Wiley-Interscience. ISBN 0-471-05059-8. Zbl 0836.14001.
- Harris, Joe (1995). Algebraic Geometry A First Course. Springer-Verlag. ISBN 0-387-97716-3. Zbl 0779.14001.
- Mumford, David (1995). Algebraic Geometry I Complex Projective Varieties (2nd ed.). Springer-Verlag. ISBN 3-540-58657-1. Zbl 0821.14001.
- Reid, Miles (1988). Undergraduate Algebraic Geometry. Cambridge University Press. ISBN 0-521-35662-8. Zbl 0701.14001.
- Shafarevich, Igor (1995). Basic Algebraic Geometry I Varieties in Projective Space (2nd ed.). Springer-Verlag. ISBN 0-387-54812-2. 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 0-387-94680-2. 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, 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. Vol. 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.
- Textbooks and references for schemes
- Eisenbud, David; Harris, Joe (1998). The Geometry of Schemes. Springer-Verlag. ISBN 0-387-98637-5. 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. Vol. 1 (2nd ed.). Springer-Verlag. ISBN 3-540-05113-9. Zbl 0203.23301.
- Hartshorne, Robin (1977). Algebraic Geometry. Springer-Verlag. ISBN 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 ed.). Springer-Verlag. ISBN 3-540-63293-X. Zbl 0945.14001.
- Shafarevich, Igor (1995). Basic Algebraic Geometry II Schemes and complex manifolds (2nd ed.). Springer-Verlag. ISBN 3-540-57554-5. Zbl 0797.14002.
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وصلات خارجية
- Foundations of Algebraic Geometry by Ravi Vakil, 764 pp.
- Algebraic geometry 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