Dawei Chen
Published 2008-08-26Version 1
Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3, P^4 or a smooth quadric threefold in P^4 respectively. Those bounds make sense from the asymptotic viewpoint if we fix d and let g vary. Some examples are constructed using determinantal varieties to show the sharpness of the bounds for d and g in a certain range. The results can also be applied to study rigid curves.
Comments: 15 pages, comments are welcome
On the Hilbert scheme of smooth curves in $\mathbb{P}^4$ of degree $d = g+1$ and genus $g$ with negative Brill-Noether number
Questions of Connectedness of the Hilbert Scheme of Curves in ${\mathbb P}^3$
Irreducibility of the Hilbert scheme of smooth curves in $\Bbb P^4$ of degree $g+2$ and genus $g$
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