Introduction to Algebraic Geometry

Code: MA623 | L-T-P-C: 3-0-0-6

 Prerequisites: MA521 (Modern Algebra) or equivalent

Filtrations, graded rings, graded modules; Krull dimension, depth, going up and going down, primary ideals, prime avoidance theorem, primary decomposition; Hilbert functions, regular local rings, Cohen-Macaulay rings; Zariski topology, Hilbert Nullstellensatz, spectrum of a ring, affine algebraic sets, affine variety, projective variety; Noether normalization, integral closure; algebraic curves, function field of a curve, divisors, principal divisors, Picard group, divisor class group, genus; monomial orderings, division algorithm, Groebner basis, syzygies.

Texts/References:

1. M. F. Atiyah & I. Macdonald, Commutative Algebra, Addison-Wesley, 1969
2. I. Shafarevich, Basic Algebraic Geometry, Springer, 1972
3. D. Eisenbud, Commutative Algebra, Springer, 1995
4. 4.R. Hartshone, Algebraic Geometry, Springer, 1997
5. J. Harris, Algebraic Geometry: A First Course, Springer, 1995
6. E. Kunz, Introduction To Commutative Algebra And Algebraic Geometry, Birkhauser, 1984