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This is a Quantitative Study study.

October 3, 2025Open Access

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

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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Heuberger et al. (Thu,) studied this question.

www.synapsesocial.com/papers/68e040f7a99c246f578b3dd5 — DOI: https://doi.org/10.5802/afst.1829

Authors

Liana Heuberger

Andrea Petracci

Journals

Annales de la faculté des sciences de Toulouse Mathématiques

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

Key Points

Abstract

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Discussion

Cite this study

Authors

Journals

Actions

References and Citations

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