K-stability of Casagrande–Druel varieties.

Cheltsov, Ivan; Duarte Guerreiro, Tiago; Fujita, Kento; Krylov, Igor; Martinez-Garcia, Jesus

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.

LOGICAL prediction; CLASSIFICATION; FAMILIES

Journal für die Reine und Angewandte Mathematik, 2025, Vol 2025, Issue 818, p53

0075-4102

Academic Journal

10.1515/crelle-2024-0074