Affine hyperplane arrangements and Jordan classes

We study the geometry of the stratification induced by an affine hyperplane ar- rangement 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 codi- mension 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 G that are normal. In the simply-connected case, we show that normality of such a quotient is equivalent to its smoothness.