We study the geometry of the stratification induced by an affine hyperplane arrangement on the quotient of a complex affine space by the action of a discrete group preserving . We give conditions ensuring normality or normality in codimension 1 of strata. We apply these results to retrieve the list of the categorical quotients of closures of Jordan classes and of sheets in a complex simple algebraic group that are normal. In the simply-connected case, we show that normality of such a quotient is equivalent to its smoothness.
Cite this article
Giovanna Carnovale, Francesco Esposito, Affine hyperplane arrangements and Jordan classes. J. Comb. Algebra 4 (2020), no. 4, pp. 397–446DOI 10.4171/JCA/48