Instructor: Dr. Andras NEMETHI
Text: your class notes
R. Shafarevich: Basic Algebraic Geometry 1 and 2, Springer Verlag 1977, 1994.
M.F. Atiyah, I.G. MacDonald: Commutative Algebra, Addison-Wesley Publ. Comp. 1969
M. Reid: Undergraduate Commutative Algebra, London Math. Soc. Students Texts 29, Cambridge Univ. Press 1995.
J. Harris: Algebraic Geometry, A First Course, Graduate Texts in Math. 133, Springer- Verlag New York, 1992
Ph. Griffiths, J. Harris: Principles of Algebraic Geometry, John Wiley & Sons, Inc., 1978
R. Hartshorne: Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag
Prerequisite: basic group theory, basic ring theory (ideals, modules
over rings, localizations, primary decomposition), field theory, formal
- Systems of algebraic equations
- Affine algebraic sets
- Correspondance between algebraic subsets and ideals
- Morphisms of affine algebraic varieties
- Irreducible algebraic sets and rational functions
- Projective algebraic varieties
- Morphisms of projective algebraic varieties
- Quasi-projective algebraic sets
- Projective algebraic plane curves
- Bezout theorem and a group law on a plane cubic curve
- Divisors on algebraic plane curves
- Divisor class group
- Divisor class group of the cubic curve =============================================== .