Orthogonal bundles on curves and theta functions
Annales de l'Institut Fourier, Volume 56 (2006) no. 5, pp. 1405-1418.

Let be the moduli space of principal SO r -bundles on a curve C, and the determinant bundle on . We define an isomorphism of H 0 (,) onto the dual of the space of r-th order theta functions on the Jacobian of C. This isomorphism identifies the rational map || * defined by the linear system || with the map |rΘ| which associates to a quadratic bundle (E,q) the theta divisor Θ E . The two components + and - of are mapped into the subspaces of even and odd theta functions respectively. Finally we discuss the analogous question for Sp 2r -bundles.

Soient l’espace des modules des fibrés SO r -principaux sur une courbe C, et le fibré déterminant sur . Nous définissons un isomorphisme de H 0 (,) sur le dual de l’espace des fonctions thêta du r-ième ordre sur la Jacobienne de C. Cet isomorphisme identifie l’application rationnelle || * définie par le système linéaire || avec l’application |rΘ| qui associe à un fibré quadratique (E,q) le diviseur thêta Θ E . Les deux composantes + et - de sont envoyées sur les sous-espaces de fonctions paires et impaires respectivement. Finalement nous discutons le problème analogue pour les fibrés symplectiques.

DOI: 10.5802/aif.2216
Classification: 14H60
Keywords: Principal bundles, orthogonal bundles, symplectic bundles, theta divisors, generalized theta functions, Verlinde formula, strange duality
Beauville, Arnaud 1

1 Université de Nice Laboratoire J.A. Dieudonné Parc Valrose 06108 Nice Cedex 2 (France)
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Beauville, Arnaud. Orthogonal bundles on curves and theta functions. Annales de l'Institut Fourier, Volume 56 (2006) no. 5, pp. 1405-1418. doi : 10.5802/aif.2216. http://archive.numdam.org/articles/10.5802/aif.2216/

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