Algebraic Geometry I. — AGE

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 =============================================== .