Picard groups on moduli of K3 surfaces with Mukai models

Francois Greer; Zhiyuan Li; Zhiyu Tian

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arXiv · 1402.2330

Picard groups on moduli of K3 surfaces with Mukai models

Francois Greer·Zhiyuan Li·Zhiyu Tian

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Abstract

We discuss the Picard group of moduli space $\mathcal{K}_g$ of quasi-polarized K3 surfaces of genus $g\leq 12$ and $g\neq 11$. In this range, $\mathcal{K}_g$ is unirational and a general element in $\mathcal{K}_g$ is a complete intersection with respect to a vector bundle on a homogenous space, by the work of Mukai. In this paper, we find generators of the Picard group $Pic_\mathbb{Q}(\mathcal{K}_g)$ using Noether-Lefschetz theory. This verifies the Noether-Lefschetz conjecture on moduli of K3 surfaces in these cases.

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BibTeX RIS

Francois Greer, Zhiyuan Li, Zhiyu Tian. 2014-02-10. Picard groups on moduli of K3 surfaces with Mukai models. https://arxiv.org/abs/1402.2330

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