K-Moduli of Fano Threefolds of Family 3.3
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917016675287040 |
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| author | Etxabarri-Alberdi, Erroxe Jones, James Matthew Papazachariou, Theodoros Stylianos |
| author_facet | Etxabarri-Alberdi, Erroxe Jones, James Matthew Papazachariou, Theodoros Stylianos |
| contents | We explicitly fully describe the K-moduli space of Fano threefold family number 3.3. We first show that K-semistable Fano varieties with volume greater than 18 are Gorenstein canonical and admit general elephants, decreasing the bound on a result by Liu and Zhao. Combining this with the moduli-continuity method via lattice-polarized K3 surfaces, we identify the K-moduli stack parametrising K-semistable varieties in family number 3.3 with a Kirwan blow up of the natural GIT quotient of $(1,1,2)$ divisors in $\mathbb{P}^1\times \mathbb{P}^1\times \mathbb{P}^2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_13611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | K-Moduli of Fano Threefolds of Family 3.3 Etxabarri-Alberdi, Erroxe Jones, James Matthew Papazachariou, Theodoros Stylianos Algebraic Geometry 14J45, 14J30, 32Q20 We explicitly fully describe the K-moduli space of Fano threefold family number 3.3. We first show that K-semistable Fano varieties with volume greater than 18 are Gorenstein canonical and admit general elephants, decreasing the bound on a result by Liu and Zhao. Combining this with the moduli-continuity method via lattice-polarized K3 surfaces, we identify the K-moduli stack parametrising K-semistable varieties in family number 3.3 with a Kirwan blow up of the natural GIT quotient of $(1,1,2)$ divisors in $\mathbb{P}^1\times \mathbb{P}^1\times \mathbb{P}^2$. |
| title | K-Moduli of Fano Threefolds of Family 3.3 |
| topic | Algebraic Geometry 14J45, 14J30, 32Q20 |
| url | https://arxiv.org/abs/2510.13611 |