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Turkish Journal of Mathematics

Authors

EDOARDO BALLICO

DOI

10.3906/mat-1911-106

Abstract

For all integers $n, d, g$ such that $n\ge 4$, $d\ge n+1$, and $(n+2)(d-n-1)\ge n(g-1)$, we define a good (i.e. generically smooth of dimension $(n+1)d+(3-n)(g-1)$ and with the expected number of moduli) irreducible component $A(d,g;n)$ of the Hilbert scheme of smooth and nondegenerate curves in $\mathbb{P}^n$ with degree $d$ and genus $g$. For most of these $(d,g)$, we prove that a general $X\in A(d,g;n)$ has maximal rank. We cover, in this way, a range of $(d,g,n)$ outside the Brill-Noether range.

First Page

423

Last Page

444

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Mathematics Commons

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