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.
Heuberger, L., Petracci, A. (2025). On K-moduli of Fano threefolds with degree 28 and Picard rank 4. ANNALES DE LA FACULTÉ DES SCIENCES DE TOULOUSE., 34(4), 1159-1184 [10.5802/afst.1829].
On K-moduli of Fano threefolds with degree 28 and Picard rank 4
Petracci, Andrea
2025
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.File in questo prodotto:
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