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 degreee. Let Q := Quot(C/C)(E, k, d) denote the Quot scheme of quotients of E of rank k and degreed. Fork > 0 and d >> 0, we compute the Picard group of Q.