Prym Subvarieties P λ 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.

Let π:ZX 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 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 λμ on Y λ ×Y μ and calculate the pull-back of ϕ μ by S λμ in terms of ϕ λ .

Soit π:ZX 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 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 λμ sur le produit des courbes Y λ ×Y μ . On calcule le pull-back de ϕ μ par S λμ en termes de ϕ λ .

DOI: 10.5802/afst.1259
Pandey, Yashonidhi 1

1 Chennai Mathematical Institute, Plot No H1, Sipcot IT Park, Padur Post Office, Siruseri 603103, India
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Pandey, Yashonidhi. 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. http://archive.numdam.org/articles/10.5802/afst.1259/

[1] Beauville (A.) and Narasimhan (M. S.) and Ramanan (S.).— Spectral curves and the generalised theta divisor, Journal für die Reine und Angewandte Mathematik, Volume 398, p. 169-179 (1989). | MR | Zbl

[2] Birkenhake (C.) and Lange (H.).— Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Volume 302, Second edition, Springer-Verlag, Berlin (2004). | MR | Zbl

[3] Donagi (R.).— Decomposition of spectral covers, Journées de Géométrie Algébrique d’Orsay (Orsay, 1992), Astérisque, 218, p. 145-175 (1993). | MR | Zbl

[4] Kanev (V.).— Spectral curves, simple Lie algebras, and Prym-Tjurin varieties, Theta functions–Bowdoin 1987, Part 1 (Brunswick, ME, 1987), Proc. Sympos. Pure Math., Volume 49, p. 627-645, Amer. Math. Soc. | MR | Zbl

[5] Kanev (V.).— Spectral curves and Prym-Tjurin varieties. I, Abelian varieties (Egloffstein, 1993), p. 151-198, de Gruyter, Berlin (1995). | MR | Zbl

[6] Lange (H.) and Kanev (V.).— Polarization type of isogenous Prym-Tyurin Varieties; Preprint (2007), Contemp. Math., Volume 465, p. 147-174, Amer. Math. Soc. (2008). | MR | Zbl

[7] Lange (H.) and Pauly (C.).— Polarizations of Prym varieties for Weyl groups via Abelianization, Journal of the European Mathematical Society, Volume 11, No. 2, p. 315-349 (2009). | MR | Zbl

[8] Lange (H.) and Recillas (S.).— Polarizations of Prym varieties of pairs of coverings, Archiv der Mathematik, Volume 86, 2, p. 111-120 (2006). | MR | Zbl

[9] Mérindol (J.-Y.).— Variétés de Prym d’un revêtement galoisien, Journal für die Reine und Angewandte Mathematik, Volume 461, p. 49-61 (1995). | MR | Zbl

[10] Mumford (D.).— Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, No. 5, Published for the Tata Institute of Fundamental Research, Bombay (1970). | MR | Zbl

[11] Mumford (D.).— Prym varieties. I, Contributions to analysis (a collection of papers dedicated to Lipman Bers), p. 325-350, Academic Press, New York (1974). | MR | Zbl

[12] Springer (T. A.).— A construction of representations of Weyl groups, Inventiones Mathematicae, Volume 44, Number 3, p. 279-293 (1978). | MR | Zbl

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