An Invitation to Algebraic Geometry, by Karen Smith,
Lauri Kahanpää, Pekka Kekäläinen, 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.
The Rising Sea, Foundations of Algebraic Geometry, by Ravi Vakil.
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 Tuesday January 16
Chapter 2, Section 2 #14,16,17,18,19
Homework 2: Due Monday January 29
Chapter 2, Section 1 #18, Section 5 #1,3,4
Homework 3: Due Monday February 5
Chapter 2, Section 5 #5,7,8,9
Homework 4: Due Monday February 12
Chapter 2, Section 5 #10,11,13,14
Homework 5: Due Monday February 19
Chapter 2, Section 5 #15,16,17,18,
Homework 6: Due Monday February 26
Section 6 #1,8, Section 7 #1, and 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 Monday March 4
Chapter 2, Section 6 #5,10, Section 7 #2,3
Homework 8: Due Monday March 11
Chapter 2, Section 7 #4,5,6, Section 8 #1
Homework 9 (this is also the final exam): Due Friday March 22
Chapter 2, Section 8 #2,3,4,5