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arXiv · 2510.13611

K-Moduli of Fano Threefolds of Family 3.3

Erroxe Etxabarri-Alberdi·James Matthew Jones·Theodoros Stylianos Papazachariou
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Abstract

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 $\mathbb{P}^1\times \mathbb{P}^1\times \mathbb{P}^2$.

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Erroxe Etxabarri-Alberdi, James Matthew Jones, Theodoros Stylianos Papazachariou. 2025-10-15. K-Moduli of Fano Threefolds of Family 3.3. https://arxiv.org/abs/2510.13611

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