K-stability and birational models of moduli of quartic K3 surfaces
K-stability and birational models of moduli of quartic K3 surfaces
复制标题
DOI：
10.1007/s00222-022-01170-5
复制
发表时间：
2021-08
影响因子：
3.1
通讯作者：
Kenneth Ascher;Kristin DeVleming;Yuchen Liu
中科院分区：
文献类型：
--
作者：
Kenneth Ascher;Kristin DeVleming;Yuchen Liu
本文证明了四次曲面的对数Fano对的K-模空间在区间（0，1）内插于四次曲面的GIT模空间和四次K3曲面模的Baily-Borel紧化之间.我们完全描述了这些K-模空间的壁交叉。作为主要的应用，我们验证Laza-O 'Grady的预测上的Hassett-Keel-Looijenga程序的四次K3曲面。我们还得到了四次二重体的K模紧化，并对四次二重体的Gorenstein正则Fano退化进行了分类。
We show that the K-moduli spaces of log Fano pairswhereSis a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily–Borel compactification of moduli of quartic K3 surfaces ascvaries 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.