Hassett--Keel Program in genus four
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |