An interpolation problem for the normal bundle of curves of genus g ≥ 2 and high degree in ℙr. Issue 2 (1st February 2017) - Ballico, E.
ABSTRACT: Let C  ⊂ ℙ n be a smooth curve and N C its normal bundle. N C satisfies strong interpolation if for all integers s  > 0 and λ i  ∈ {0, 1, …, n −1}, 1 ≤  i  ≤  s, there are distinct points P 1, …, P s ∈ C and linear subspaces U i ⊆ E | P i such that dim ( U i ) = n − 1 − λ i for all i and a certain map H 0 ( E ) → ⊕ i = 1 s ( E | P i ) ∕ U i 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  ≥ (5 n −8) g  + 2 n 2 −5 n  + 4 of a smooth curve X of genus g  ≥ 2.