JournalsjemsVol. 11, No. 2pp. 315–349

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
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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.

Cite this article

Christoph Scheven, Christian Pauly, Polarizations of Prym varieties for Weyl groups via abelianization. J. Eur. Math. Soc. 11 (2009), no. 2, pp. 315–349

DOI 10.4171/JEMS/152