Math 203A, Fall 2021

Professor

Elham Izadi ; AP&M 6240 ; phone: 858-534-2638 ; email: eizadi@ucsd.edu ; Office hours: Mondays 14:00-15:00, Thursdays 14:00-15:00
Lectures: Tuesday, Thursday 11:00-12:20

Course description

This is the first quarter of the introductory sequence in Algebraic Geometry. We will cover some of Chapters 1 and 2 of Hartshorne's book, as time permits. We will, in particular, define varieties and schemes and their basic properties.

Prerequisites

MATH 200 A-B-C

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.
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

09/23/2021 09/28/2021 09/30/2021 10/05/2021 10/07/2021 10/12/2021 10/14/2021 10/19/2021 10/21/2021 10/26/2021 10/28/2021 11/02/2021 11/04/2021 11/09/2021 11/16/2021 11/18/2021 11/23/2021 11/30/2021 12/02/2021

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. Late homework will not be accepted. Homework will normally be due one week after it is assigned, usually on a Tuesday. 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 two days, until the Thursday office hour, to read and comment on the homework that is assigned to you as reviewer. At the Thursday office hour, we will go over some of the solutions to the homework.

Homework assigments

Homework 1: Due Tuesday October 5
Chapter 1, Section 1 #1,2,4,5,6

Homework 2: Due Tuesday October 12
Chapter 1, Section 1 #7,8,9,10 ; Chapter 1, Section 2 #1

Homework 3: Due Tuesday October 19
Chapter 1, Section 2 #2,6,7,8,10 (also do #9 but do not turn it in)

Homework 4: Due Tuesday October 26
Chapter 2, Section 1 #1,2,3,4,5

Homework 5: Due Tuesday November 2
Chapter 2, Section 1 #6,7,8,17,22

Homework 6: Due Tuesday November 09
Chapter 2, Section 1 #9
Chapter 2, Section 2 #1,2,3,5

Homework 7: Due Tuesday November 16
Chapter 2, Section 2 #6,7,8,9,12

Homework 8: Due Tuesday November 23
Chapter 2, Section 3 #1,2,3,4,5

Homework 9: Due Tuesday November 30
Chapter 2, Section 3, #6,7,8,9,10

Homework 10 (this is also the final exam): Due Thursday December 9
Chapter 2, Section 4, #1,2,3,4,6 and 11 if you want to try something a little harder (Section 32.14 of the Stacks project, on universally closed morphisms, might be helpful for this)

Elham Izadi
Last modified: Thu Dec 16 10:52:58 PST 2021