Stable pair compactification of moduli of K3 surfaces of degree 2-Reference-Cited by-同舟云学术

Stable pair compactification of moduli of K3 surfaces of degree 2

Published:2023-04-20 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Alexeev Valery¹,Engel Philip¹,Thompson Alan²

Affiliation:

1. Department of Mathematics , University of Georgia , Athens , GA 30602 , USA

2. Department of Mathematical Sciences , Loughborough University , Loughborough , Leicestershire, LE11 3TU , United Kingdom

Abstract

Abstract We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable KSBA pairs ( X , ϵ ⁢ R )

(X,\epsilon R)

over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of K3 surfaces in this family are described by integral-affine structures on a sphere with 24 singularities.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2023-0011/pdf

Reference55 articles.

1. V. Alexeev, Moduli spaces M g , n ⁢ ( W ) M_{g,n}(W) for surfaces, Higher-dimensional complex varieties (Trento 1994), De Gruyter, Berlin (1996), 1–22.

2. V. Alexeev, Complete moduli in the presence of semiabelian group action, Ann. of Math. (2) 155 (2002), no. 3, 611–708.

3. V. Alexeev, Higher-dimensional analogues of stable curves, International congress of mathematicians. Vol. II, European Mathematical Society, Zürich (2006), 515–536.

4. V. Alexeev, Moduli of weighted hyperplane arrangements, Adv. Courses Math. CRM Barcelona, Birkhäuser/Springer, Basel 2015.

5. V. Alexeev, A. Brunyate and P. Engel, Compactifications of moduli of elliptic K3 surfaces: Stable pair and toroidal, preprint (2019), https://arxiv.org/abs/2002.00712; to appear in Geom. Topol.

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Compact moduli of K3 surfaces with a nonsymplectic automorphism;Transactions of the American Mathematical Society, Series B;2024-01-22

2. Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces;Mathematische Nachrichten;2023-09-22

3. Compact moduli of elliptic K3 surfaces;Geometry & Topology;2023-07-27

4. Special Lagrangian Fibrations, Berkovich Retraction, and Crystallographic Groups;International Mathematics Research Notices;2023-03-23