Math 203B, Winter 2024


Elham Izadi ; AP&M 6240 ; phone: 858-534-2638 ; email: ; Office hours: Thursdays 13:00-14:00 and Fridays 14:00-15:00 in room AP&M 6218
Lectures: Tueday, Thursday 11:00-12:20

Course description

This is the second quarter of the introductory sequence in Algebraic Geometry. We will cover some of Chapters 2, 3 and 4 of Hartshorne's book, as time permits.




Algebraic Geometry, By Robin Hartshorne


The litterature on Algebraic Geometry is staggering. Here are a few books but you can find many more with some basic google searches.

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.

Class Notes

01/09/2024 01/11/2024 01/16/2024 01/18/2024 01/23/2024 01/25/2024 01/30/2024 02/01/2024 02/06/2024 02/08/2024 02/13/2024 02/15/2024 02/20/2024 02/22/2024 02/27/2024 02/29/2024 03/05/2024 03/07/2024 03/12/2024 03/14/2024


There will be weekly homework assignments (posted below, but subject to change during the quarter). Please submit your homework online to Canvas as a pdf file by the due time and date. Homework will normally be due one week after it is assigned, usually on a Monday. On the due date of a homework assignment, Canvas will automatically assign two of you as reviewers for each homework. The reviewers will write comments for the homework that they read. You will have three days, until the Thursday office hour, to read and comment on the homework that is assigned to you as reviewer. During the Thursday office hour, we will go over some of the solutions to the homework.

Homework assigments

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

Elham Izadi
Last modified: Mon Mar 18 10:16:18 PDT 2024