Stability of Picard sheaves for vector bundles on curves

Abstract For a stable vector bundle E of slope μ ( E ) > 2 g − 1 on a smooth, projective curve of genus g , we show that the Picard sheaf E ˆ on the Picard variety of the curve is stable. We introduce a homological tool for testing semistability of Picard sheaves. We also obtain the semistability of the general Picard sheaf if μ ( E ) ∈ [ g − 2 , g ] , μ ( E ) ≠ g − 1 .