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

• 成果类型: Article
• 署名作者: Ascher, Kenneth; DeVleming, Kristin; Liu, Yuchen
• 署名单位: University of California System; University of California Irvine; University of Massachusetts System; University of Massachusetts Amherst; Northwestern University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01170-5
• 发表日期: 2023
• 页码: 471-552
• 关键词: kahler-einstein metrics; fano varieties; rational connectedness; stable curves; SPACE; compactifications; arrangements; Boundedness; EXISTENCE; families

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.