Affine hyperplane arrangements and Jordan classes

Pub Date : 2018-07-27 DOI:10.4171/jca/48
G. Carnovale, F. Esposito
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引用次数: 2

Abstract

We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in codimension 1 of strata. As an application, we provide the list of those categorical quotients of closures of Jordan classes and of sheets in all complex simple algebraic groups that are normal. In the simply connected case, we show that normality of such a quotient is equivalent to its smoothness.
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仿射超平面排列与Jordan类
我们研究了复仿射空间商上的仿射超平面排列H在保持H的离散群的作用下引起的分层的几何性质。我们给出了保证层的余维1正态性或正态性的条件。作为一个应用,我们提供了Jordan类的闭包和所有正规复单代数群中的表的范畴商的列表。在简单连通的情况下,我们证明了这种商的正规性等价于它的光滑性。
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