We prove the following statement, which has been conjectured since 1985: There exists a constant K such that for all natural numbers d, g with g⩽Kd3/2 there exists an irreducible component of the Hilbert scheme of P3 whose general element is a smooth, connected curve of degree d and genus g of maximal rank.

Maximal rank of space curves in the range A / Ballico, Edoardo; Ellia, Philippe; Fontanari, Claudio. - In: EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 2199-675X. - 2018, 4:3(2018), pp. 778-801. [10.1007/s40879-018-0235-z]

Maximal rank of space curves in the range A

Edoardo Ballico;Claudio Fontanari
2018-01-01

Abstract

We prove the following statement, which has been conjectured since 1985: There exists a constant K such that for all natural numbers d, g with g⩽Kd3/2 there exists an irreducible component of the Hilbert scheme of P3 whose general element is a smooth, connected curve of degree d and genus g of maximal rank.
2018
3
Ballico, Edoardo; Ellia, Philippe; Fontanari, Claudio
Maximal rank of space curves in the range A / Ballico, Edoardo; Ellia, Philippe; Fontanari, Claudio. - In: EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 2199-675X. - 2018, 4:3(2018), pp. 778-801. [10.1007/s40879-018-0235-z]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/206922
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