An interpolation problem for the normal bundle of curves of genus g = 2 and high degree in P-r

摘要

Let CPn be a smooth curve and N-C its normal bundle. N-C satisfies strong interpolation if for all integers s>0 and (i){0,1,...,n-1}, 1is, there are distinct points such that for all i and a certain map has maximal rank (Atanasov). We prove that N-C satisfies strong interpolation if either C is a linearly normal elliptic curve or C is a general embedding of degree d(5n-8)g+2n(2)-5n+4 of a smooth curve X of genus g >= 2.