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- Title
K-stability of Casagrande–Druel varieties.
- Authors
Cheltsov, Ivan; Duarte Guerreiro, Tiago; Fujita, Kento; Krylov, Igor; Martinez-Garcia, Jesus
- Abstract
We introduce a new subclass of Fano varieties (Casagrande–Druel varieties) that are 푛-dimensional varieties constructed from Fano double covers of dimension n − 1 . We conjecture that a Casagrande–Druel variety is K-polystable if the double cover and its base space are K-polystable. We prove this for smoothable Casagrande–Druel threefolds, and for Casagrande–Druel varieties constructed from double covers of P n − 1 ramified over smooth hypersurfaces of degree 2 d with n > d > n 2 > 1 . As an application, we describe the connected components of the K-moduli space parametrizing smoothable K-polystable Fano threefolds in the families № 3.9 and № 4.2 in the Mori–Mukai classification.
- Subjects
LOGICAL prediction; CLASSIFICATION; FAMILIES
- Publication
Journal für die Reine und Angewandte Mathematik, 2025, Vol 2025, Issue 818, p53
- ISSN
0075-4102
- Publication type
Academic Journal
- DOI
10.1515/crelle-2024-0074