Polarizations of Prym varieties for Weyl groups via abelianization

Lange, Herbert, and Pauly, Christian. "Polarizations of Prym varieties for Weyl groups via abelianization." Journal of the European Mathematical Society 011.2 (2009): 315-349. <http://eudml.org/doc/277294>.

@article{Lange2009,
abstract = {Let $\pi :Z\rightarrow X$ 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 $Y=Z/\mathrm \{Stab\}(\lambda )$. 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 $\mathrm \{Jac\}(Y)$ 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 $X$.},
author = {Lange, Herbert, Pauly, Christian},
journal = {Journal of the European Mathematical Society},
keywords = {Prym variety; principal $G$-bundle; abelianization; moduli stack; Galois covering of smooth projective curves; abelian subvariety of the Jacobian; canonical principal polarization; Prym-Tyurin varieties; Donagi-Prym variety},
language = {eng},
number = {2},
pages = {315-349},
publisher = {European Mathematical Society Publishing House},
title = {Polarizations of Prym varieties for Weyl groups via abelianization},
url = {http://eudml.org/doc/277294},
volume = {011},
year = {2009},
}

TY - JOUR
AU - Lange, Herbert
AU - Pauly, Christian
TI - Polarizations of Prym varieties for Weyl groups via abelianization
JO - Journal of the European Mathematical Society
PY - 2009
PB - European Mathematical Society Publishing House
VL - 011
IS - 2
SP - 315
EP - 349
AB - Let $\pi :Z\rightarrow X$ 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 $Y=Z/\mathrm {Stab}(\lambda )$. 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 $\mathrm {Jac}(Y)$ 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 $X$.
LA - eng
KW - Prym variety; principal $G$-bundle; abelianization; moduli stack; Galois covering of smooth projective curves; abelian subvariety of the Jacobian; canonical principal polarization; Prym-Tyurin varieties; Donagi-Prym variety
UR - http://eudml.org/doc/277294
ER -