ORBIT PARAMETRIZATIONS FOR K3 SURFACES

被引：7

作者：

Bhargava, Manjul ^{[1
]}

Ho, Wei ^{[2
]}

Kumar, Abhinav ^{[3
,4
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[3] MIT, Dept Math, Cambridge, MA 02139 USA

[4] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA

来源：

FORUM OF MATHEMATICS SIGMA | 2016年 / 4卷

基金：

美国国家科学基金会;

关键词：

SALEM-NUMBERS; AUTOMORPHISMS; RINGS; REPRESENTATIONS; DISCRIMINANTS; RATIONALITY; INVARIANTS; DYNAMICS; ENTROPY; DENSITY;

D O I：

10.1017/fms.2016.12

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits of a representation are in bijection with K3 surfaces (up to suitable equivalence) whose Neron-Severi lattice contains a given lattice. An immediate consequence is that the corresponding moduli spaces of these lattice-polarized K3 surfaces are all unirational. Our constructions also produce many fixed-point-free automorphisms of positive entropy on K3 surfaces in various families associated to these representations, giving a natural extension of recent work of Oguiso.

引用

页数：86

共 75 条

[1]

[Anonymous], B AM MATH SOC

[2]

[Anonymous], CLASSICAL ALGEBRAIC

[3]

[Anonymous], 2006, Moduli Spaces and Arithmetic Geometry, Adv. Stud. Pure Math., V45, P315

[4]

Arbarello E., 1985, GEOMETRY ALGEBRAIC C, V267, DOI 10.1007/978-1-4757-5323-3

[5]