Picard groups on moduli of K3 surfaces with Mukai models

Francois Greer, Zhiyuan Li, Zhiyu Tian

We discuss the Picard group of moduli space ${\mathcal{K}}_g$ of quasi-polarized K3 surfaces of genus $g\le 12$ and $g\ne 11$. In this range, ${\mathcal{K}}_g$ is unirational and a g…