# M 390 C Algebraic Geometry Spring, 2009

INSTRUCTOR: Felipe Voloch
(RLM 9.122, ph.471-2674, )
CLASS HOURS AND LOCATION: (NOTE CHANGE!)
MWF 1:00 -- 2:00, RLM 12.166

UNIQUE NUMBER: 57315

OFFICE HOURS: Wed 9:30 -- 11:00 or by appointment.

TEXTBOOK: K. Hulek,
Elementary Algebraic Geometry, AMS 2003.
Errata.

PREREQUISITES: Graduate Algebra.
Contact me if you have any questions about prerequisites.

GRADE POLICY: A few problems will be assigned as homework. Students will
also be asked to grade one of their classmates' homework.

HOMEWORK ASSIGNMENT: Do problem 3 of every chapter (including ch. 0).
Due 04/10/09.

COURSE DESCRIPTION:
Algebraic Geometry deals with sets of solutions of polynomial
equations in several variables and various generalizations of this
concept. It is a huge subject which has been central to major developments
in modern Mathematics. This course will be a gentle introduction to the
basic ideas of Algebraic Geometry. The plan is to cover the material in
the textbook and, if time permits, give a proof of the Riemann-Roch theorem
for curves.

## Topics to be covered

- Affine varieties
- Projective varieties
- Smooth points and dimension
- Plane cubic curves
- Cubic surfaces
- Introduction to the theory of curves
- The Riemann-Roch theorem

## Links

- Fulton's book
Algebraic Curves is now available for download. It's a good alternative
text for the course.

- Nice discussion on Tao's blog on
the Ax-Grothendieck theorem.