Families of lattice-polarized K3 surfaces

Algebra Seminar
Monday, November 18, 2013 - 16:05
1 hour (actually 50 minutes)
Skiles 006
Columbia University
There are well-known explicit families of K3 surfaces equipped with a low degree polarization, e.g., quartic surfaces in P^3. What if one specifies multiple line bundles instead of a single one? We will discuss representation-theoretic constructions of such families, i.e., moduli spaces for K3 surfaces whose Neron-Severi groups contain specified lattices. These constructions, inspired by arithmetic considerations, also involve some fun geometry and combinatorics. This is joint work with Manjul Bhargava and Abhinav Kumar.