Math 130c: Algebraic Geometry

Lectures: Tuesday and Thursday at 2:30-4pm
Instructor: Amin Gholampour
Email address: agholamp@caltech.edu
Office: Sloan 258
Office Hour: any time
The course description:
This is the continuation of Math 130b and 130a. Most of the materials in the first two chapters of Hartshorne's book are assumed. I will try to be more concrete in this course by spending most of the time on curves and surfaces. I will try to cover some parts of chapters 3, 4 and 5 of Hartshorne's book.

Some references:
Algebraic Geometry by Hartshorne
The Geometry of schemes by Eizenbud & Harris
The red book of varieties and schemes by Mumford
Algebraic Geometry by Iitaka
Algebraic Geometry 1, 2, 3 by Ueno
Principles of Algebraic Geometry by Griffiths and Harris
Introduction to commutative algebra by Atiyah & Macdonald
Commutative Algebra by Matsumura
An introduction to homological algebra by Weibel

Suggested Homework:

1st week	Hartshorne: II.1.16.(b), II.1.16.(c), II.5.6.(d), III.3.1, III.3.2, III.4.1, III.4.7
2nd week	Compute the dim H^r (X, O(n) ) where X is a projective hypersurface corresponding to an irreducible homogeneous polynomial. Hartshorne: III.5.1, III.8.3, III.8.4.a), III.8.4.b), I II.8.4.c)
3rd week	Hartshorne: III.4.2
4th week	Hartshorne: II.6.2, III.5.3.a), III.5.3.b)
5th week	Hartshorne: II.7.7, III.7.1, IV.1.5, IV.1.6, IV.1.7.a)
6th week	Hartshorne: IV.1.2, IV.2.5, IV.3.1
7th week	Hartshorne: IV.3.2, IV.5.2, V.1.1, V.1.2, V.1.3.a)
8th week	Hartshorne: V.2.6, V.3.7.a) , b), V.5.2, A.6.7