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Polarizations of Prym varieties for Weyl groups via abelianization

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Herbert Lange, Christian Pauly (I3M)

Algebraic Geometry · Submitted 2 Feb 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We compute the type of the polarization of the restriction of the canonical principal polarization of $\Jac(Y)$ to $P_\lambda$ in some cases.

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arXiv IDmath/0702055 (version 2)
Pith IDYH2YU3RS, Pith's permanent record of this paper and its review
CitationChristian Pauly (I3M), Herbert Lange. "Polarizations of Prym varieties for Weyl groups via abelianization." arXiv:math/0702055 (2007). https://pith.science/paper/YH2YU3RS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,922 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.57 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.07 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

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 $X$.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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 $G$. background 0.97 0.10 0.02 asserted 0.87
s1 For any dominant weight $\lambda$ consider the curve $Y = Z/\Stab(\lambda)$. background 0.47 0.19 0.03 asserted 0.68
s2 The Kanev correspondence defines an abelian subvariety $P_\lambda$ of the Jacobian of $Y$. background 0.92 0.10 0.05 asserted 1.00
s3 We compute the type of the polarization of the restriction of the canonical principal polarization of $\Jac(Y)$ to $P_\lambda$ in some cases. result 0.83 0.95 0.36 asserted 0.97
s4 In particular, in the case of the group $E_8$ we obtain families of Prym-Tyurin varieties. result 0.99 0.93 0.23 asserted 1.00
s5 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 $X$. method 0.99 0.57 0.11 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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 $X$.

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