On K-moduli of Fano threefolds with degree 28 and Picard rank 4
We analyse the local structure of the K-moduli space of Fano varieties at a toric singular K-polystable Fano <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> </mml:math> -fold, which deforms to smooth Fano <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> </mml:math> -folds with anticanonical volume <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>28</mml:mn> </mml:math> and Picard rank <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>4</mml:mn> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> </mml:math> -folds is a rational surface.
Authors
- Andrea Petracci (ORCID: https://orcid.org/0000-0003-4837-3431)
- Liana Heuberger (ORCID: https://orcid.org/0000-0002-8038-9620)
Institutions
- Institut de Mathématiques de Marseille (FR)
- Institut Polytechnique de Bordeaux (FR)
- University of Bologna (IT)
Publication Details
- Journal
- Annales de la faculté des sciences de Toulouse Mathématiques
- Published
- 2025-10-02
- DOI
- https://doi.org/10.5802/afst.1829
- Primary Topic
- Geometry and complex manifolds
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Leverhulme Trust
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni