Moduli of Genus Six Curves and K-stability

Junyan Zhao

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arXiv · 2212.06992

Moduli of Genus Six Curves and K-stability

Junyan Zhao

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Abstract

The K-moduli theory provides a different compactification of moduli spaces of curves. As a general genus six curve can be canonically embedded into the smooth quintic del Pezzo surface, we study in this paper the K-moduli spaces $\overline{M}^K(c)$ of the quintic log Fano pairs. We classify the strata of genus six curves $C$ appearing in the K-moduli by explicitly describing the wall-crossing structure. The K-moduli spaces interpolate between two birational moduli spaces constructed by GIT and moduli of K3 surfaces via Hodge theory.

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Junyan Zhao. 2022-12-14. Moduli of Genus Six Curves and K-stability. https://arxiv.org/abs/2212.06992

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