Hassett--Keel Program in genus four

Fuente: arXiv
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Main Authors: Ascher, Kenneth, DeVleming, Kristin, Liu, Yuchen, Wang, Xiaowei
Format: Preprint
Published: 2025
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_version_ 1866910921650077696
author Ascher, Kenneth
DeVleming, Kristin
Liu, Yuchen
Wang, Xiaowei
author_facet Ascher, Kenneth
DeVleming, Kristin
Liu, Yuchen
Wang, Xiaowei
contents The Hassett--Keel program seeks to give a modular interpretation to the steps of the log minimal model program of $\overline{\mathcal{M}}_g$. The goal of this paper is to complete the Hassett--Keel program in genus four, supplementing earlier results of Casalaina-Martin--Jensen--Laza and Alper--Fedorchuk--Smyth--van der Wyck. The main tools we use are wall crossing for moduli spaces of pairs in the sense of K-stability and KSBA stability, and the recently constructed moduli spaces of boundary polarized Calabi--Yau surface pairs. We also give a construction of the hyperelliptic flip using a stackified Chow quotient which is expected to generalize to higher genus.
format Preprint
id arxiv_https___arxiv_org_abs_2504_20312
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Hassett--Keel Program in genus four
Ascher, Kenneth
DeVleming, Kristin
Liu, Yuchen
Wang, Xiaowei
Algebraic Geometry
14H10
The Hassett--Keel program seeks to give a modular interpretation to the steps of the log minimal model program of $\overline{\mathcal{M}}_g$. The goal of this paper is to complete the Hassett--Keel program in genus four, supplementing earlier results of Casalaina-Martin--Jensen--Laza and Alper--Fedorchuk--Smyth--van der Wyck. The main tools we use are wall crossing for moduli spaces of pairs in the sense of K-stability and KSBA stability, and the recently constructed moduli spaces of boundary polarized Calabi--Yau surface pairs. We also give a construction of the hyperelliptic flip using a stackified Chow quotient which is expected to generalize to higher genus.
title Hassett--Keel Program in genus four
topic Algebraic Geometry
14H10
url https://arxiv.org/abs/2504.20312