In this paper we prove that, for any n ≥ 3, there exist infinitely many r ∈ N and for each of them a smooth, connected curve Crin ℙrsuch that Crlies on exactly n irreducible components of the Hilbert scheme Hilb(ℙr). This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.
On the Hilbert scheme of curves in higher-dimensional projective space / Fantechi, Barbara; Pardini, Rita. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 90:1(1996), pp. 1-15. [10.1007/BF02568289]
On the Hilbert scheme of curves in higher-dimensional projective space
Fantechi, Barbara;
1996-01-01
Abstract
In this paper we prove that, for any n ≥ 3, there exist infinitely many r ∈ N and for each of them a smooth, connected curve Crin ℙrsuch that Crlies on exactly n irreducible components of the Hilbert scheme Hilb(ℙr). This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.File in questo prodotto:
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