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K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES
Published online by Cambridge University Press: 16 September 2021
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.
MSC classification
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 3 , May 2023 , pp. 1251 - 1291
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
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