## ANNOUNCEMENTS

- Registration for Fall term opens Thursday, May 19, 2016.
- This page was last updated: .

## 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.

## 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

## 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 | |