General stable bundles arising as normal bundles of projective curves

Abstract

Let X be a smooth projective curve of genus g ³2. For all integers r, d with r>0 let M(X;r,d) be the moduli scheme of rank r stable vector bundles on X with degree d. Here we prove that for all integers n,d with n³3 and d ³(5n-8)g + 2n2-5n+4 there is an open dense subset W of M(X; n-1, (n+1)d +2g-2) such that for every N I W there is a non-degenerate degree d embedding of X in Pn with N as normal bundle. For the proof we use reducible smoothable curves.