A Vanishing Theorem for the Twisted Normal Bundle of Curves in P^n, n8. Issue 1 (30th March 2020) - Ballico, E.
Abstract: We prove the existence of a smooth and non-degenerate curve XP^n, n8, with (X)=d, p_a(X)=g, h^1(N_X(-1))=0, and general moduli for all (d, g, n) such that d(n-3)g/2 ceil +n+3 . It was proved by C. Walter that, for n4, the inequality 2d(n-3)g+4 is a necessary condition for the existence of a curve with h^1(N_X(-1))=0 .