# Polarizations of Prym varieties for Weyl groups via abelianization

Herbert Lange; Christian Pauly

Journal of the European Mathematical Society (2009)

- Volume: 011, Issue: 2, page 315-349
- ISSN: 1435-9855

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topLange, 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 -

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