Ivan, Cheltsov and Tiago, Duarte Guerreiro and Kento, Fujita and Igor, Krylov and Martinez-Garcia, Jesus (2024) K-stability of Casagrande--Druel varieties. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal. DOI https://doi.org/10.1515/crelle-2024-0074
Ivan, Cheltsov and Tiago, Duarte Guerreiro and Kento, Fujita and Igor, Krylov and Martinez-Garcia, Jesus (2024) K-stability of Casagrande--Druel varieties. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal. DOI https://doi.org/10.1515/crelle-2024-0074
Ivan, Cheltsov and Tiago, Duarte Guerreiro and Kento, Fujita and Igor, Krylov and Martinez-Garcia, Jesus (2024) K-stability of Casagrande--Druel varieties. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal. DOI https://doi.org/10.1515/crelle-2024-0074
Abstract
We introduce a new subclass of Fano varieties (Casagrande-Druel varieties), that are n-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 2d with n>d>n2>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.
Item Type: | Article |
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Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 16 Oct 2024 10:39 |
Last Modified: | 30 Oct 2024 19:00 |
URI: | http://repository.essex.ac.uk/id/eprint/39102 |
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Filename: 10.1515_crelle-2024-0074.pdf
Licence: Creative Commons: Attribution 4.0