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K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES

Part of: Surfaces and higher-dimensional varieties Families, fibrations

Published online by Cambridge University Press:  16 September 2021

Kenneth Ascher Open the ORCID record for Kenneth Ascher [Opens in a new window] ,
Kristin Devleming  and
Yuchen Liu Open the ORCID record for Yuchen Liu [Opens in a new window]
Kenneth Ascher*
Affiliation:
Department of Mathematics, University of California – Irvine, 340 Rowland Hall, Irvine, CA 92697, USA
Kristin Devleming
Affiliation:
Department of Mathematics, University of California – San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA (kdevleming@ucsd.edu)
Yuchen Liu
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA (yuchenl@northwestern.edu)
*
kascher@uci.edu
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Abstract

We show that the K-moduli spaces of log Fano pairs $\left(\mathbb {P}^1\times \mathbb {P}^1, cC\right)$ , where C is a $(4,4)$ curve and their wall crossings coincide with the VGIT quotients of $(2,4)$ , complete intersection curves in $\mathbb {P}^3$ . This, together with recent results by Laza and O’Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of $(4,4)$ curves on $\mathbb {P}^1\times \mathbb {P}^1$ and the Baily–Borel compactification of moduli of quartic hyperelliptic K3 surfaces.

Keywords

K-modulimoduliK3 surfacesvariation of GIT

MSC classification

Primary: 14J10: Families, moduli, classification 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14D23: Stacks and moduli problems
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 3 , May 2023 , pp. 1251 - 1291
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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