JournalsjemsVol. 11 , No. 2DOI 10.4171/jems/152

Polarizations of Prym varieties for Weyl groups via abelianization

  • Christoph Scheven

    Friedrich-Alexander-Universität Erlangen, Germany
  • Christian Pauly

    Université de Montpellier II, France
Polarizations of Prym varieties for Weyl groups via abelianization cover

Abstract

Let π:Z\raX\pi: Z \ra X be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group GG. For any dominant weight λ\lambda consider the curve Y=Z/\Stab(λ)Y = Z/\Stab(\lambda). The Kanev correspondence defines an abelian subvariety PλP_\lambda of the Jacobian of YY. We compute the type of the polarization of the restriction of the canonical principal polarization of \Jac(Y)\Jac(Y) to PλP_\lambda in some cases. In particular, in the case of the group E8E_8 we obtain families of Prym-Tyurin varieties. The main idea is the use of an abelianization map of the Donagi-Prym variety to the moduli stack of principal GG-bundles on the curve XX.