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 elements in the classical cases and arbitrary elements of gln(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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 903-922 |
| Number of pages | 20 |
| Journal | Selecta Mathematica, New Series |
| Volume | 19 |
| Issue number | 4 |
| DOIs | |
| State | Published - Nov 2013 |
Funding
The author would like to thank her advisor, Sam Evens, for suggesting this problem and giving many valuable comments. Thanks also to the anonymous referee for helpful suggestions, including a clarification of the notation in Sect. 4. The work for this project was partially supported by the NSA.
Keywords
- Affine paving
- Bruhat decomposition
- Hessenberg varieties
ASJC Scopus subject areas
- General Mathematics
- General Physics and Astronomy