The Moduli Space of Genus Six Curves and K-stability: VGIT and the Hassett-Keel Program

2023/04/26 by Zhao, Junyan
#14H10 #14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.13259

Abstract

A general curve C of genus six is canonically embedded into the smooth del Pezzo surface Σ⊆ ℙ¹ × ℙ² of degree 5 as a divisor in the class O_Σ(2,2). In this article, we study the variation of geometric invariant theory (VGIT) for such pairs (Σ,C), and relate the VGIT moduli spaces to the K-moduli of pairs (Σ,C) and the Hassett-Keel program for moduli of genus six curves. We prove that the K-moduli spaces M^K(c) give the final several steps in the Hassett-Keel program for M₆.

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