The boundary of K-moduli of prime Fano threefolds of genus twelve
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911579823407104 |
|---|---|
| author | Kaloghiros, Anne-Sophie Liu, Yuchen Petracci, Andrea Zhao, Junyan |
| author_facet | Kaloghiros, Anne-Sophie Liu, Yuchen Petracci, Andrea Zhao, Junyan |
| contents | We study the K-moduli stack of prime Fano threefolds of genus twelve, known as $V_{22}$. We prove that its boundary, which parametrizes singular members, is purely divisorial and consists of four irreducible components corresponding to the four families of Prokhorov's one-nodal $V_{22}$.
A key ingredient is a modular relation between Fano threefolds $X$ and their anticanonical K3 surfaces $S$. We prove that the forgetful morphism from the moduli of Fano--K3 pairs $(X,S)$ where $X$ is a K-semistable degeneration of $V_{22}$ to the moduli space of genus $12$ polarized K3 surfaces $(S,{-K_X}|_S)$ is an open immersion. In particular, the K-moduli of $V_{22}$ is governed by the moduli of their anticanonical K3 surfaces, providing a modular realization of Mukai's philosophy. Along the way, we develop a general deformation framework for Fano threefolds of large volume, which may be useful beyond the study of K-moduli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29827 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The boundary of K-moduli of prime Fano threefolds of genus twelve Kaloghiros, Anne-Sophie Liu, Yuchen Petracci, Andrea Zhao, Junyan Algebraic Geometry Differential Geometry We study the K-moduli stack of prime Fano threefolds of genus twelve, known as $V_{22}$. We prove that its boundary, which parametrizes singular members, is purely divisorial and consists of four irreducible components corresponding to the four families of Prokhorov's one-nodal $V_{22}$. A key ingredient is a modular relation between Fano threefolds $X$ and their anticanonical K3 surfaces $S$. We prove that the forgetful morphism from the moduli of Fano--K3 pairs $(X,S)$ where $X$ is a K-semistable degeneration of $V_{22}$ to the moduli space of genus $12$ polarized K3 surfaces $(S,{-K_X}|_S)$ is an open immersion. In particular, the K-moduli of $V_{22}$ is governed by the moduli of their anticanonical K3 surfaces, providing a modular realization of Mukai's philosophy. Along the way, we develop a general deformation framework for Fano threefolds of large volume, which may be useful beyond the study of K-moduli. |
| title | The boundary of K-moduli of prime Fano threefolds of genus twelve |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2603.29827 |