Stability of the Picard Bundle

Abstract

Let X be a non‐singular algebraic curve of genus g ⩾ 2, n ⩾ 2 an integer, ξ a line bundle over X of degree d > 2n(g − 1) with (n,d) = 1 and Mξ the moduli space of stable bundles of rank n and determinant ξ over X. It is proved that the Picard bundle Wξ is stable with respect to the unique polarisation of Mξ. 2000 Mathematics Subject Classification 14H60, 14J60.