On the symmetric algebra of stable vector bundles on curves

Let X be a smooth projective curve of genus g greater than or equal to 2 an d E a general stable vector bundle on X with rank(E) = r and deg(E) = d > 0 . Let z be the smallest integer with zd > 2gr. Here we study the graded alg ebra H-0(X, Sym(E)) := circle plus H-n greater than or equal to0(0)(X, S-n( E)) and prove that it is generated by elements of degree less than or equal to z.