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October 3, 2025Annales de la faculté des sciences de Toulouse Mathématiques0 citationsOpen Access

On K-moduli of Fano threefolds with degree 28 and Picard rank 4

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LHLiana HeubergerAix-Marseille UniversitéAPAndrea PetracciImperial College London

Key Points

  • The irreducible component of K-moduli parametrizing smooth Fano 3-folds is identified as a rational surface.
  • Constructing an algebraic deformation of the toric singular Fano leads to insights about K-moduli space.
  • Analysis focuses on Fano varieties that deform to smooth Fano 3-folds with specific degrees and structural properties.
  • Understanding the local structure of K-moduli can influence our knowledge of Fano varieties and their classifications.

Abstract

We analyse the local structure of the K-moduli space of Fano varieties at a toric singular K-polystable Fano 3-fold, which deforms to smooth Fano 3-folds with anticanonical volume 28 and Picard rank 4. In particular, by constructing an algebraic deformation of this toric singular Fano, we show that the irreducible component of K-moduli parametrising these smooth Fano 3-folds is a rational surface.

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Cite This Study

Heuberger et al. (2025) studied this question.

synapsesocial.com/papers/68e040f7a99c246f578b3dd5https://doi.org/10.5802/afst.1829
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