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 11
Chapter 2, Section 2 #14,16,17,18,19
Homework 2: Due Tuesday January 18
Chapter 2, Section 1 #18, Section 5 #1,3,5
Homework 3: Due Tuesday January 25
Chapter 2, Section 5 #4,7, optional: #8,9
Homework 4: Due Tuesday February 1
Chapter 2, Section 5 #10,12, optional: #11, 13
Homework 5: Due Tuesday February 8
Chapter 2, Section 5 #17, optional: #14,15,16,18 (note: mainly read
these carefully and make sure you understand the statements, in many
textbooks these are done in the text)
Homework 6: Due Tuesday February 15
Chapter 2, Section 6 #1,8, Section 7 #1
Optional: 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 Tuesday February 22
Chapter 2, Section 6 #5, Section 7 #2, optional: Section 6 #10, Section 7 #3
Homework 8: Due Tuesday March 1
Chapter 2, Section 7 #4,5,8,9
Homework 9: Due Tuesday March 8
Chapter 2, Section 8 #1,2,3
Homework 10: Due Tuesday March 15
Optional: Chapter 2, Section 8 #4, 5
Final Exam: Due Tuesday March 15
Chapter 2, Section 8 #2