An invitation to algebraic geometry, by Karen Smith,
Lauri Kahanp"a"a, Pekka Kek"al"ainen, William Traves.
The red book of varieties and schemes, by David Mumford.
Principles of algebraic geometry, by Phillip Griffiths and
Joseph Harris.
Complex algebraic surfaces, by Arnaud Beauville.
Algebraic geometry, a first course, by Joseph Harris.
Geometry of Schemes, by David Eisenbud and Joseph Harris.
Algebraic Geometry, An Introduction, by Daniel Perrin.
Algebraic geometry, by Igor Shafarevich.
Introduction to Algebraic Geometry, by Brendan Hassett.
Introduction to commutative algebra, by Michael Atiyah and
Ian McDonald.
Commutative algebra, By H. Matsumura.
Commutative Algebra with a view toward algebraic geometry,
by David Eisenbud.
Homework 1: Due Thursday January 19
Chapter 2, Section 2 #14,16,17,18,19
Homework 2: Due Thursday January 26
Chapter 2, Section 4, #1,2,3,4,6
Homework 3: Due Thursday February 2
Chapter 2, Section 5 #1,3,4,5,7
Homework 4: Due Thursday February 9
Chapter 2, Section 5 #8,9,10,11,13
Homework 5: Due Thursday February 16
Chapter 2, Section 5 #14,15,16,17,18 (note: these problems are
especially hard but also especially important and interesting, do as
much of them as you can, only please make sure you read them carefully
and understand the statements, in many textbooks these are done in the
text)
Homework 6: Due Thursday February 23
Chapter 2, Section 6 #1,8, Section 7 #1, Also prove the following:
If X is integral, then any nonzero morphism of invertible sheaves is
injective, any generically injective morphism of locally free sheaves
is injective (hint: first prove that a locally free sheaf has no
torsion subsheaf, where by a torsion sheaf we mean a sheaf whose
support has codimension > 0).
Homework 7: Due Thursday March 2
Chapter 2, Section 6 #5,10, Section 7 #2,3
Homework 8: Due Thursday March 9
Chapter 2, Section 7 #4,5,7,8,9
Homework 9: Due Thursday March 16
Chapter 2, Section 8 #1,2,3