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

Kenneth Ascher*, Kristin DeVleming, Yuchen Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that the K-moduli spaces of log Fano pairs (P3, 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 P3.

Original languageEnglish (US)
Pages (from-to)471-552
Number of pages82
JournalInventiones Mathematicae
Issue number2
StatePublished - May 2023

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'K-stability and birational models of moduli of quartic K3 surfaces'. Together they form a unique fingerprint.

Cite this