Affine pavings of Hessenberg varieties for semisimple groups
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Martha Precup [1]
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[1] University of Notre Dame
University of Notre Dame
Township of Portage, Estados Unidos
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 19, Nº. 4, 2013, págs. 903-922
- Idioma: inglés
- Enlaces
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Resumen
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)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.
