JournalsjcaVol. 4, No. 4pp. 397–446

Affine hyperplane arrangements and Jordan classes

  • Giovanna Carnovale

    University of Padova, Italy
  • Francesco Esposito

    University of Padova, Italy
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Abstract

We study the geometry of the stratification induced by an affine hyperplane arrangement H\mathcal H on the quotient of a complex affine space by the action of a discrete group preserving H\mathcal H. 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 GG 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. 397–446

DOI 10.4171/JCA/48