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European Journal of Mathematics

, Volume 4, Issue 3, pp 778–801 | Cite as

Maximal rank of space curves in the range A

  • Edoardo Ballico
  • Philippe Ellia
  • Claudio Fontanari
Research Article
  • 24 Downloads

Abstract

We prove the following statement, which has been conjectured since 1985: There exists a constant K such that for all natural numbers dg with \(g\leqslant Kd^{3/2}\) there exists an irreducible component of the Hilbert scheme of \(\mathbb {P}^3\) whose general element is a smooth, connected curve of degree d and genus g of maximal rank.

Keywords

Space curve Postulation Hilbert function Hilbert scheme 

Mathematics Subject Classification

14H50 14N05 

Notes

Acknowledgements

We thank the anonymous referee for useful comments.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Edoardo Ballico
    • 1
  • Philippe Ellia
    • 2
  • Claudio Fontanari
    • 1
  1. 1.Dipartimento di MatematicaUniversità di TrentoTrentoItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di FerraraFerraraItaly

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