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Mathematics
Algebraic Geometry
1. Foundations of Algebraic Geometry
2. Polynomial Rings and Commutative Algebra
3. Gröbner Bases
4. Affine Algebraic Geometry
5. Projective Algebraic Geometry
6. Rational Maps and Birational Geometry
7. Local Properties and Singularities
8. Introduction to Schemes
9. Coherent Sheaves and Cohomology
10. Divisors and Line Bundles
11. Algebraic Curves
12. Algebraic Surfaces
13. Advanced Topics
3.
Gröbner Bases
3.1.
Motivation and Applications
3.1.1.
Solving Polynomial Systems
3.1.2.
Ideal Membership Problem
3.1.3.
Elimination Theory
3.2.
Buchberger's Algorithm
3.2.1.
S-polynomials
3.2.2.
Reduction Process
3.2.3.
Algorithm Description
3.2.4.
Termination and Correctness
3.3.
Applications of Gröbner Bases
3.3.1.
Elimination of Variables
3.3.2.
Implicitization
3.3.3.
Solving Polynomial Systems
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2. Polynomial Rings and Commutative Algebra
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4. Affine Algebraic Geometry