K-Moduli of Fano Threefolds of Family 3.3

Fuente: arXiv
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Main Authors: Etxabarri-Alberdi, Erroxe, Jones, James Matthew, Papazachariou, Theodoros Stylianos
Format: Preprint
Published: 2025
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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
id 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