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arXiv · 1205.3976

Affine pavings of Hessenberg varieties for semisimple groups

Martha Precup
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Abstract

In this paper we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. We prove that Hessenberg varieties corresponding to nilpotent elements which are regular in a Levi factor are paved by affines. We provide a partial reduction from paving Hessenberg varieties for arbitrary elements to paving those corresponding to nilpotent elements. As a consequence, we generalize results of Tymoczko asserting that Hessenberg varieties for regular nilpotent and arbitrary elements of \mathfrak{gl}_n(\C) are paved by affines. For example, our results prove that any Hessenberg variety corresponding to a regular element is paved by affines. As a corollary, in all these cases the Hessenberg variety has no odd dimensional cohomology.

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Martha Precup. 2012-05-17. Affine pavings of Hessenberg varieties for semisimple groups. https://arxiv.org/abs/1205.3976

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