海森伯格理想纤维的仿射铺装

arXiv: Algebraic Geometry Pub Date : 2020-07-17 DOI:10.13016/EVQM-0Y32

Ke Xue

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引用次数: 3

摘要

我们定义了旗子纤维的某些闭合子纤维，并证明了它们是由仿射铺成的。黑森伯格理想纤维是对施普林格纤维的自然推广。在$G_2$型中，我们给出了所有Hessenberg理想纤维的显式描述，研究了它们的一些几何性质，并用它们完全分类了Weyl群在正则半单Hessenberg簇上同调上的Tymoczko点作用。

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Affine Pavings of Hessenberg Ideal Fibers

We define certain closed subvarieties of the flag variety, Hessenberg ideal fibers, and prove that they are paved by affines. Hessenberg ideal fibers are a natural generalization of Springer fibers. In type $G_2$, we give explicit descriptions of all Hessenberg ideal fibers, study some of their geometric properties and use them to completely classify Tymoczko's dot actions of the Weyl group on the cohomology of regular semisimple Hessenberg varieties.

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arXiv: Algebraic Geometry

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