The name "K3 surface" was introduced by Andre Weil in honor of three
algebraic geometers, Kummer, Kahler and Kodaira, and the mountain K2 in
Kashmir.
This
course aims to give an introduction to the geometry of K3 surfaces,
focusing on a few selected
topics. In particular, I hope to discuss the following:
- examples of K3 surfaces
- elliptic K3 surfaces
- linear systems on K3s
- Hodge structures
- periods and Torelli
- the moduli space of K3s
- the tautological ring.
(This may be a bit too ambitious for a one quarter course, so the
goals
may change slightly as we go.)