Picard Groups on Moduli of K3 Surfaces with Mukai Models

被引：15

作者：

Greer, Francois ^{[1
]}

Li, Zhiyuan ^{[1
]}

Tian, Zhiyu ^{[2
]}

机构：

[1] Stanford Univ, Dept Math, Bldg 380, Stanford, CA 94305 USA

[2] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2015年 / 2015卷 / 16期

关键词：

PROJECTIVE MODELS; SPACE;

D O I：

10.1093/imrn/rnu152

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the Picard group of the moduli space K-g of quasi-polarized K3 surfaces of genus g <= 12 and g not equal 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 for the Picard group PicQ(K-g) using the Noether-Lefschetz (NL) theory. This verifies the NL conjecture on the moduli of K3 surfaces in these cases.

引用

页码：7238 / 7257

页数：20