K-polystability of Fano 4-folds with large Lefschetz defect
Algebraic Geometry
2025-12-16 v2 Differential Geometry
Abstract
In this paper, we investigate K-polystability on smooth complex Fano 4-folds with Lefschetz defect at least 2, focusing on the case of Lefschetz defect 3 and on Casagrande-Druel Fano 4-folds with Lefschetz defect 2. We show that exactly 5 of the 19 families of Fano 4-folds with Lefschetz defect 3 are K-polystable. Moreover, among 175 families of Casagrande-Druel Fano 4-folds with Lefschetz defect 2, we prove that 5 are K-polystable, while 132 are K-unstable.
Cite
@article{arxiv.2409.03571,
title = {K-polystability of Fano 4-folds with large Lefschetz defect},
author = {Eleonora A. Romano and Saverio A. Secci},
journal= {arXiv preprint arXiv:2409.03571},
year = {2025}
}
Comments
Added Theorem 1.2 and sections 5-6 on Casagrande-Druel Fano 4-folds; 20 pages