On the Hilbert function of general unions of curves in projective spaces

2020/05/08 by Ballico, Edoardo
#14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.03880

Abstract

Let X=X₁∪ ⋯ ∪ X_s⊂ \mathbb Pⁿ, n≥ 4, be a general union of smooth non-special curves with X_i of degree d_i and genus g_i and d_i≥ max \2g_i-1,g_i+n\ if g_i>0. We prove that X has maximal rank, i.e. for any t∈ \mathbb N either h⁰(I_X(t))=0 or h¹(I_X(t))=0.

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