On the Hilbert scheme of curves in higher-dimensional projective space |
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Authors: | Barbara Fantechi Rita Pardini |
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Institution: | (1) Dipartimento di Matematica, Via Sommarive, 14-I 38050 Povo (Trento), Italy;(2) Dipartimento di Matematica e Informatica, Via delle Scienze, 206-I 33100 Udine, Italy |
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Abstract: | In this paper we prove that, for anyn≥3, there exist infinitely manyr∈N and for each of them a smooth, connected curveC
r in ℙ
r
such thatC
r lies on exactlyn 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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Keywords: | |
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