Interpolation for normal bundles of general curves

2015/09/05 by Atanasov, Atanas, Larson, Eric, Yang, David · 3 citations
#14H99 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.01724

Abstract

Given n general points p₁, p₂,..., p_n in P^r, it is natural to ask when there exists a curve C ⊂ P^r, of degree d and genus g, passing through p₁, p₂,..., p_n. In this paper, we give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle N_C of a general nonspecial curve of degree d and genus g in P^r (with d >= g + r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H⁰(N_C(-D)) = 0 or H¹(N_C(-D)) = 0), with exactly three exceptions.

Cited by

• Restricted tangent bundle of rational curves on projective hypersurfaces
• The Harder-Narasimhan Filtration of a Trigonal Canonical Curve
• Stability of normal bundles of Brill--Noether curves in ℙ⁴

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