K-moduli of curves on a quadric surface and K3 surfaces

Kenneth Ascher; Kristin DeVleming; Yuchen Liu

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arXiv · 2006.06816

K-moduli of curves on a quadric surface and K3 surfaces

Kenneth Ascher·Kristin DeVleming·Yuchen Liu

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Abstract

We show that the K-moduli spaces of log Fano pairs $(\mathbb{P}^1\times\mathbb{P}^1, cC)$ 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-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.

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Kenneth Ascher, Kristin DeVleming, Yuchen Liu. 2020-06-11. K-moduli of curves on a quadric surface and K3 surfaces. https://arxiv.org/abs/2006.06816

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