Author:
Ascher Kenneth,DeVleming Kristin,Liu Yuchen
Abstract
AbstractWe show that the K-moduli spaces of log Fano pairs $$({\mathbb {P}}^3, cS)$$
(
P
3
,
c
S
)
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 $${\mathbb {P}}^3$$
P
3
.
Publisher
Springer Science and Business Media LLC
Reference105 articles.
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