Fano and weak Fano Hessenberg varieties
Algebraic Geometry
2020-03-30 v1 Combinatorics
Representation Theory
Abstract
Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety which is a toric variety. We give a complete classification of Fano and weak Fano regular semisimple Hessenberg varieties in type A in terms of combinatorics of Hessenberg functions. In particular, we show that if the anti-canonical bundle of a regular semisimple Hessenberg variety is nef, then it is in fact nef and big.
Keywords
Cite
@article{arxiv.2003.12286,
title = {Fano and weak Fano Hessenberg varieties},
author = {Hiraku Abe and Naoki Fujita and Haozhi Zeng},
journal= {arXiv preprint arXiv:2003.12286},
year = {2020}
}
Comments
42 pages, 14 figures