Polarizations of Prym varieties for Weyl groups via abelianization

• Autores: Herbert Lange, Christian Pauly
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 11, Nº 2, 2009, págs. 315-349
• Idioma: inglés
• DOI: 10.4171/jems/152
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• Resumen

  • Let $\pi: Z \ra X$ be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group $G$. For any dominant weight $\lambda$ consider the curve $Y = Z/\Stab(\lambda)$. The Kanev correspondence defines an abelian subvariety $P_\lambda$ of the Jacobian of $Y$. We compute the type of the polarization of the restriction of the canonical principal polarization of $\Jac(Y)$ to $P_\lambda$ in some cases. In particular, in the case of the group $E_8$ 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 $G$-bundles on the curve $X$.