Stability and deformations of generalised Picard sheaves

Abstract

Let C be a smooth irreducible complex projective curve of genus $$g \ge 2$$ and M the moduli space of stable vector bundles on C of rank n and degree d with $$\gcd (n,d)=1$$ . A generalised Picard sheaf is the direct image on M of the tensor product of a universal bundle on $$M\times C$$ 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 $$g\ge 3$$ , $$n\ge 2$$ (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.