Projective Curves With Nice Normal Bundles and Containing a Prescribed Subset of a Hyperplane - Ballico, Edoardo (Sarajevo Journal of Mathematics, 2022)
Fix a hyperplane HP^n, n>3, and a finite set SH. We give conditions on the integers d, g and (S) such that there exists a smooth and connected curve XP^n with (X) =d, p_a(X)=g and SXH. When d=(S) we may take g up to order 2d/n, d0, when S is in linear general position. We also prove the existence of X with h^1(N_X(-1))=0 if n8, g is odd and 2d(n-3)g+n+11.