K-Moduli of Fano Threefolds of Family 3.3

2025/10/15 by Erroxe Etxabarri-Alberdi, Etxabarri-Alberdi, Erroxe, Theodoros Stylianos Papazachariou +2
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2510.13611

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 ℙ¹× ℙ¹× ℙ².

Citations

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• Existence of minimal models for varieties of log general type
• Mirror symmetry for lattice polarized K3 surfaces

Related

• K-moduli of Fano threefolds and genus four curves
• K-moduli of Fano threefolds in family 3.10
• On K-moduli of Fano threefolds with degree 28 and Picard rank 4
• K-moduli of Fano 3-folds can have embedded points
• On the compactified moduli space of Family 2.24