Stability and deformations of generalised Picard sheaves

Let C be a smooth irreducible complex projective curve of genus g ≥ 2 and M the moduli space of stable vector bundles on C of rank n and degree d with (n,d)=1 . A generalised Picard sheaf is the direct image on M of the tensor product of a universal bundle on M× C by the pullback of a vector bundle E_0 on C . In this paper, we investigate the stability of generalised Picard sheaves and, in the case where these are locally free, their deformations. When g≥ 3 , n≥ 2 (with some additional restrictions for g=3,4 ) and the rank and degree of E_0 are coprime, this leads to the construction of a fine moduli space for deformations of Picard bundles.