Picard Groups of Some Quot Schemes

Abstract Let C be a smooth projective curve over the field of complex numbers C of genus g (C) 0. Let E be a locally free sheaf on C of rank r and degree e. Let Q: =Quot₂/₂ (E, k, d) denote the Quot scheme of quotients of E of rank k and degree d. For k0 and d 0, we compute the Picard group of Q.