A duality for Spin Verlinde spaces and Prym theta functions C Pauly and S Ramanan

Niveau: Supérieur, Master, Bac+4
A duality for Spin Verlinde spaces and Prym theta functions C. Pauly and S. Ramanan August 29, 2000 Abstract We prove canonical isomorphisms between Spin Verlinde spaces,i.e., spaces of global sec- tions of a determinant line bundle over the moduli space of semistable Spinn-bundles over a smooth projective curve C, and the dual spaces of theta functions over Prym varieties of unramified double covers of C. 1 Introduction To any smooth, projective curve C, one classically associates a collection of principally polarized abelian varieties: the Jacobian JC, parametrizing degree zero line bundles, as well as, for any unramified double cover C˜? ? C, depending on a non-zero 2-torsion point ? ? JC[2], a Prym variety P?. The projective geometry of the configuration JC ? ? ? P? has been much studied [M1], [vGP], [B1] and encodes e.g. the Schottky-Jung identities among theta-constants [M1]. Less classically, one can consider the moduli space M(G) of semistable principal G-bundles over the curve C, where G is a simple and simply-connected algebraic group. For some ample line bundle L over M(G), the vector space of global sections H0(M(G),L) has been identified to a space of conformal blocks arising in conformal field theory (see e.

• theta


• line bundle


• divisors associated


• associated half-spinor


• any smooth


• spinor vector


• spin group


• bundles over


• prym varieties