*Instructor:* Dr. Andras NEMETHI

*Text:* your class notes

*Reference books:*
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
series.

*Topics:*

- 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 =============================================== .