On the Hilbert scheme of curves in higher-dimensional projective space

Details On the Hilbert scheme of curves in higher-dimensional projective space On the Hilbert scheme of curves in higher-dimensional projective space

1995-01-17

arxiv.org/abs/alg-geom/9501009v1

Mathematics

Algebraic Geometry

latex, 12 pages, no figures

Scientific paper

In this paper we prove that, for any $n\ge 3$, there exist infinitely many
$r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such
that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme
$\hilb(\P^r)$. This is proven by reducing the problem to an analogous
statement for the moduli of surfaces of general type.

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