GEOMETRY OF REGULAR HESSENBERG VARIETIES

GEOMETRY OF REGULAR HESSENBERG VARIETIES

Let g be a complex semisimple Lie algebra. For a regular element x in g and a Hessenberg space H ⊆ g , we consider a regular Hessenberg variety X ( x, H ) in the ag variety associated with g . We take a Hessenberg space so that X ( x, H ) is irreducible, and show that the higher cohomology groups of...

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Veröffentlicht in:Transformation groups 2020-06, Vol.25 (2), p.305-333
Hauptverfasser: ABE, HIRAKU, FUJITA, NAOKI, ZENG, HAOZHI
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Algebra
Homology
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
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description Let g be a complex semisimple Lie algebra. For a regular element x in g and a Hessenberg space H ⊆ g , we consider a regular Hessenberg variety X ( x, H ) in the ag variety associated with g . We take a Hessenberg space so that X ( x, H ) is irreducible, and show that the higher cohomology groups of the structure sheaf of X ( x, H ) vanish. We also study the flat family of regular Hessenberg varieties, and prove that the scheme-theoretic fibers over the closed points are reduced. We include applications of these results as well.
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subjects Algebra
Homology
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
title GEOMETRY OF REGULAR HESSENBERG VARIETIES
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