The Theta Divisor of $SU_C(2,2d)^s$ is very Ample if $C$ is not Hyperelliptic

Abstract

Let $X$ be the moduli space of semistable rank 2 vector bundles over a smooth curve C of genus $g \ge 2$ and $\theta : X \to PH^0(L)^*$ be the map associated to the generalized theta divisor L on X. We prove that for C not hyperelliptic, the map $\theta$ is injective and the differential of $\theta$ is injective at smooth points of X.