An interpolation problem for the normal bundle of curves of genus g ≥ 2 and high degree in ℙr. Issue 2 (1st February 2017)

• Record Type: Journal Article
• Authors: Ballico, E.
• Is Part Of: Communications in algebra. Volume 45:Issue 2(2017)
• Page Start: 822
• Page End: 827
• Publication Date: 2017-02-01
• Subjects: Curve in projective spaces -- normal bundle -- semistable vector bundle; 14H50 -- 14H60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1175584
• Languages: English
• ISSNs: 0092-7872

Abstract

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.