Ma 130a:  Algebraic Geometry (Fall 2016-17)

ANNOUNCEMENTS


COURSE DESCRIPTION

This is a first course in algebraic geometry. We will discuss briefly classical topics including affine and projective varieties. The majority of the course will be focused on the modern approach to algebraic geometry via schemes and sheaves. Familiarity with commutative algebra is highly advised.

Some of the results we will discuss are Bezout's theorem, the Nullstellensatz, the group law on an elliptic curve, blowups and birational geometry and Grassmannians.


PREREQUISITES

familiarity with basic category theory as well as commutative algebra; e.g. Atiyah-MacDonald.


SCHEDULE

MWF, 15:00 - 15:55, 153 Sloan.


INSTRUCTORS

Pablo Solis
OLGA TAUSSKY AND JOHN TODD INSTRUCTOR IN MATHEMATICS
360 Sloan
626-395-4336


TA's

TBA


OFFICE HOURS

MW from 2-3


POLICIES

Grades

The grade is based entirely on homework.

Homework Policy

In certain cases I may grant homework extensions. I highly discourage asking for a homework extension the day before or the day an assignment is due; those requests have a low probability of being granted.


TOPICS COVERED

category theory: universal properties, (co)limits. Polynomial rings, algebraic sets and the basic dictionary between algebra and geometry. Results from commutative algebra: various forms of the nullstellensatz, Noether normalization, dimension. Classical algebraic geometry: varieties over an algebraically closed field. Sheaves: defintion, stalks, morphisms of sheaves, global sections, sheafifacation. Schemes: definitions, examples. Topological and sheaf theoretic properties. Morphisms of schemes. Quasicoherent sheaves. Weil and Cartier Divisors, Picard groups.


TEXTBOOKS

I will use a mixture of Ravi Vakil's notes and Hartshorne's algebraic geometry.

The following online notes on sheaves may be helpful: Sheaves


LECTURE NOTES

Date Description
  notes
   
   

HOMEWORK

Due Date Homework Solutions
 10/03/2016   hw1  
 10/14/2016   hw2  
 10/26/2016  hw3  
  11/09/2016   hw4  
  12/07/2016   hw5  
     
     
     

EXAMS

 


READING