Abstract
Let M0 (resp. Mp) denote the moduli space parametrizing semistable rank 2 bundles with determinant equal to OC (resp. OC(p)) over a smooth, projective curve C of genus g ≥ 2; p is a fixed point of C. The Picard group of both moduli spaces is isomorphic to ZZ and we denote by L (resp. Lp) their ample generators. Then the Verlinde formula gives the dimension of the vector spaces H(M0,L) and H(Mp,Lp) which consist of what is called generalized or nonabelian theta functions of level k. Several authors have studied the geometry of the moduli space M0 in connection with the Jacobian J and the Prym variety Px of an unramified double cover of the curve C associated to a nonzero 2-torsion point x. The Kummers of all these abelian varieties can be mapped naturally to M0 and the intersection points of two distinct Kummers give the Schottky-Jung and Donagi relations between their theta-nulls [vG-P1]. As a consequence of these identities, van Geemen and Previato [vG-P
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