Affine pavings of Hessenberg varieties for semisimple groups

作者：Precup Martha^*

来源：Selecta Mathematica, New Series, 2013, 19(4): 903-922.

DOI：10.1007/s00029-012-0109-z

• Hessenberg varieties
• Affine paving
• Bruhat decomposition

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 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.

• 出版日期2013-11