Prym Subvarieties $P_\lambda $ of Jacobians via Schur correspondences between curves

Yashonidhi Pandey

doi:10.5802/afst.1259

Prym Subvarieties

P_{λ}

of Jacobians via Schur correspondences between curves

Yashonidhi Pandey ¹

¹ Chennai Mathematical Institute, Plot No H1, Sipcot IT Park, Padur Post Office, Siruseri 603103, India

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 603-633.

Abstract
Abstract

Let $π : Z \to X$ denote a Galois cover of smooth projective curves with Galois group $W$ a Weyl group of a simple Lie group $G$ . For a dominant weight $λ$ , we consider the intermediate curve $Y_{λ} = Z / Stab (λ)$ . One defines a Prym variety $P_{λ} \subset Jac (Y_{λ})$ and we denote by $ϕ_{λ}$ the restriction of the principal polarization of $Jac (Y_{λ})$ upon $P_{λ}$ . For two dominant weights $λ$ and $μ$ , we construct a correspondence $S_{λ μ}$ on $Y_{λ} \times Y_{μ}$ and calculate the pull-back of $ϕ_{μ}$ by $S_{λ μ}$ in terms of $ϕ_{λ}$ .

Soit $π : Z \to X$ un revêtement Galoisien de courbes projectives lisses de groupes de Galois $W$ un groupe de Weyl d’un groupe de Lie $G$ . Pour un poids dominant $λ$ , on considère la courbe intermediare $Y_{λ} = Z / Stab (λ)$ . On définit la variété de Prym $P_{λ} \subset Jac (Y_{λ})$ et on note par $ϕ_{λ}$ la restriction de la polarisation principale du $Jac (Y_{λ})$ à $P_{λ}$ . Pour deux poids dominants $λ$ et $μ$ , on construit une correspondence $S_{λ μ}$ sur le produit des courbes $Y_{λ} \times Y_{μ}$ . On calcule le pull-back de $ϕ_{μ}$ par $S_{λ μ}$ en termes de $ϕ_{λ}$ .

MR Zbl

DOI: 10.5802/afst.1259

Author's affiliations:

Yashonidhi Pandey ¹

¹ Chennai Mathematical Institute, Plot No H1, Sipcot IT Park, Padur Post Office, Siruseri 603103, India

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     author = {Yashonidhi Pandey},
     title = {Prym {Subvarieties} $P_\lambda $ of {Jacobians} via {Schur} correspondences between curves},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {603--633},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 19},
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Yashonidhi Pandey. Prym Subvarieties $P_\lambda $ of Jacobians via Schur correspondences between curves. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 603-633. doi : 10.5802/afst.1259. https://afst.centre-mersenne.org/articles/10.5802/afst.1259/

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