# Picard groups on Moduli space of K3 surfaces

## Zhiyuan Li (Stanford)

The Noether-Lefschetz divisors on moduli space M_2d of quasi-polarized K3 surfaces of degree 2d will be introduced from both geometry and arithmetic. Maulik and Pandharipande have conjectured that the Picard group of M_2d is generated by the Noether-Lefschetz divisors. We verify this conjecture via GIT when the degree is small. I will also talk about the general case and the relation to automorphic representation theory. A conjectural approach to this problem may be discussed at the end of this talk. This is a joint work with Zhiyu Tian.

Wednesday, April 10th, at 4:00pm in HBH 227

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