K-stability and birational models of moduli of quartic K3 surfaces

被引：5

作者：

Ascher, Kenneth ^{[1
]}

DeVleming, Kristin ^{[2
]}

Liu, Yuchen ^{[3
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

[3] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

来源：

INVENTIONES MATHEMATICAE | 2023年 / 232卷 / 02期

关键词：

KAHLER-EINSTEIN METRICS; FANO VARIETIES; RATIONAL CONNECTEDNESS; STABLE CURVES; SPACE; COMPACTIFICATIONS; ARRANGEMENTS; BOUNDEDNESS; EXISTENCE; FAMILIES;

D O I：

10.1007/s00222-022-01170-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the K-moduli spaces of log Fano pairs (P-3, cS) where S is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Borel compactification of moduli of quartic K3 surfaces as c varies in the interval (0, 1). We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza-O' Grady's prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of quartic double solids, and classify all Gorenstein canonical Fano degenerations of P-3.

引用

页码：471 / 552

页数：82

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