The Hilbert function of general unions of lines and double lines in the projective space

2021/09/12 by Ballico, Edoardo
#14H50 #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.05452

Abstract

We study the Hilbert function of a general union X⊂ ℙ³ of x double lines and y lines. In many cases (e.g. always for x=2 and y≥ 3 or for x=3 and y≥ 2 or for x≥ 4 and y≥ \lceil(\binom3x+43 -27x-12)/(3x+2)\rceil +3-x) we prove that X has maximal rank. We give a few examples of x and y for which X has not maximal rank.

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