Turkish Journal of Mathematics
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.
Keywords
Curve in projective spaces, normal bundle, Hilbert scheme, Hilbert function
First Page
423
Last Page
444
Recommended Citation
BALLICO, EDOARDO
(2021)
"Good components of curves in projective spaces outside the Brill-Noether range,"
Turkish Journal of Mathematics: Vol. 45:
No.
1, Article 25.
https://doi.org/10.3906/mat-1911-106
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss1/25
