On the Hilbert scheme of linearly normal curves in ℙ^r with small index of speciality

2021/03/30 by Keem, Changho
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14C05 #Secondary 14H10

paper · doi:10.48550/arxiv.2103.16321

Abstract

We study the Hilbert scheme H^L_d,g,r parametrizing smooth, irreducible, non-degenerate and linearly normal curves of degree d and genus g in ℙ^r whose complete and very ample hyperplane linear series D have relatively small index of speciality i(D)=g-d+r. In particular we show the existence (and non-existence as well in some sporadic cases) of every Hilbert scheme of linearly normal curves with i(D)=4. We also determine the irreducibility of H^L_2r+4,r+8,r for 3≤ r≤ 8, which are rather peculiar families in a certain sense.

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