# Math 203B, Winter 2024

### Professor

Elham Izadi ; AP&M 6240 ; phone: 858-534-2638 ;
email: eizadi@ucsd.edu ; 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.
### Prerequisites

MATH 203A
### Text

Algebraic Geometry, By Robin Hartshorne
### References

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
### Homework

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