Semitoric degenerations of Hibi varieties and flag varieties
Abstract
We construct a family of flat semitoric degenerations for the Hibi variety of every finite distributive lattice. The irreducible components of each degeneration are the toric varieties associated with polytopes forming a regular subdivision of the order polytope of the underlying poset. These components are themselves Hibi varieties. For each degeneration in our family we also define the corresponding weight polytope and embed the degeneration into the associated toric variety as the union of orbit closures given by a set of faces. Every such weight polytope projects onto the order polytope with the chosen faces projecting into the parts of the corresponding regular subdivision. We apply these constructions to obtain a family of flat semitoric degenerations for every type A Grassmannian and complete flag variety.
Keywords
Cite
@article{arxiv.2008.13243,
title = {Semitoric degenerations of Hibi varieties and flag varieties},
author = {Evgeny Feigin and Igor Makhlin},
journal= {arXiv preprint arXiv:2008.13243},
year = {2021}
}
Comments
The paper arXiv:2112.05894 should be viewed as the up-to-date version of these ideas, see also top of first page in this paper