K-polystability of Fano 4-folds with large Lefschetz defect

2024/09/05 by Romano, Eleonora A., Secci, Saverio A.
#14J35 #14J45 #32Q20 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.03571

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.

Related

• On Casagrande-Druel Fano varieties with Lefschetz defect 2
• On some Fano 4-folds with Lefschetz defect 3
• K-stability of Casagrande-Druel varieties
• The Lefschetz defect of Fano varieties
• K-stability of Fano 3-folds in the World of Null-A