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

Barbara Fantechi; Rita Pardini

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

alg-geom 2015-06-30 v1 Algebraic Geometry

Authors: Barbara Fantechi , Rita Pardini

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 $\P^r$ 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.

Keywords

Hilbert scheme projective space irreducible components moduli of surfaces smooth curves

Cite

@article{arxiv.alg-geom/9501009,
  title  = {On the Hilbert scheme of curves in higher-dimensional projective space},
  author = {Barbara Fantechi and Rita Pardini},
  journal= {arXiv preprint arXiv:alg-geom/9501009},
  year   = {2015}
}

Comments

latex, 12 pages, no figures

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