Picard groups on moduli of K3 surfaces with Mukai models

2014/02/10 by Greer, Francois, Li, Zhiyuan, Tian, Zhiyu · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.2330

Abstract

We discuss the Picard group of moduli space K_g of quasi-polarized K3 surfaces of genus g≤ 12 and g≠ 11. In this range, K_g is unirational and a general element in 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_ℚ(K_g) using Noether-Lefschetz theory. This verifies the Noether-Lefschetz conjecture on moduli of K3 surfaces in these cases.

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