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Components of the Hilbert scheme of smooth space curves with the expected number of moduli

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Abstract

For any d and g such that the Brill-Noether number ρ(d,g,3) is negative, d≥20 and g≤f(d), where f(d)=d3/2/(6·21/2) + lower order terms, there exists a regular component of H 3d,g (the closure in Hilbℙ3 of the open set parametrizing smooth, connected, non-degenerate curves in ℙ3) with the expected number of moduli. Moreover, examples of the fact that such components are not unique are given.

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  1. Dipartimento di Matematica, Università di Ferrara, Via Machiavelli, 35, 44100, Ferrara, Italy

    Giuseppe Pareschi

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  1. Giuseppe Pareschi
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Pareschi, G. Components of the Hilbert scheme of smooth space curves with the expected number of moduli. Manuscripta Math 63, 1–16 (1989). https://doi.org/10.1007/BF01173697

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