Maximal rank of space curves in the range A

2017/05/29 by Ballico, Edoardo, Ellia, Philippe, Fontanari, Claudio
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.10113

Abstract

We prove the following statement, which has been conjectured since 1985: There exists a constant K such that for all natural numbers d,g with g≤ Kd^3/2 there exists an irreducible component of the Hilbert scheme of ℙ³ whose general element is a smooth, connected curve of degree d and genus g of maximal rank.

Related

• The Maximal Rank Conjecture
• The Maximal Rank Conjecture for Sections of Curves
• Existence and the reducibility of the Hilbert scheme of linearly normal\n curves in \ℙ^r of relatively high degrees
• The maximal genus of space curves in the range A
• On the Hilbert scheme of linearly normal curves in ℙ^r of relatively high degree