K-moduli of Fano threefolds and genus four curves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910825190522880 |
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| author | Liu, Yuchen Zhao, Junyan |
| author_facet | Liu, Yuchen Zhao, Junyan |
| contents | In this article, we study the K-moduli space of Fano threefolds obtained by blowing up $\mathbb{P}^3$ along $(2,3)$-complete intersection curves. This K-moduli space is a two-step birational modification of the GIT moduli space of $(3,3)$-curves on $\mathbb{P}^1 \times \mathbb{P}^1$. As an application, we show that our K-moduli space appears as one model of the Hassett--Keel program for $\overline{M}_4$. In particular, we classify all K-(semi/poly)stable members in this deformation family of Fano varieties. We follow the moduli continuity method with moduli of lattice-polarized K3 surfaces, general elephants and Sarkisov links as new ingredients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-moduli of Fano threefolds and genus four curves Liu, Yuchen Zhao, Junyan Algebraic Geometry In this article, we study the K-moduli space of Fano threefolds obtained by blowing up $\mathbb{P}^3$ along $(2,3)$-complete intersection curves. This K-moduli space is a two-step birational modification of the GIT moduli space of $(3,3)$-curves on $\mathbb{P}^1 \times \mathbb{P}^1$. As an application, we show that our K-moduli space appears as one model of the Hassett--Keel program for $\overline{M}_4$. In particular, we classify all K-(semi/poly)stable members in this deformation family of Fano varieties. We follow the moduli continuity method with moduli of lattice-polarized K3 surfaces, general elephants and Sarkisov links as new ingredients. |
| title | K-moduli of Fano threefolds and genus four curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.16747 |