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

Barbara Fantechi·Rita Pardini
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Abstract

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 $¶^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme $\hilb(¶^r)$. This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.

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BibTeXRIS

Barbara Fantechi, Rita Pardini. 1995-01-17. On the Hilbert scheme of curves in higher-dimensional projective space. https://arxiv.org/abs/alg-geom/9501009

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