Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-20T16:27:49.091Z Has data issue: false hasContentIssue false
  • English
  • Français

Hilbert Schemes of Degree Four Curves

Published online by Cambridge University Press:  04 December 2007

Scott Nollet  and
Enrico Schlesinger
Scott Nollet
Affiliation:
Department of Mathematics, Texas Christian University, Fort Worth, TX 76129, USA. e-mail: [email protected]
Enrico Schlesinger
Affiliation:
Dipartimento di Matematica, Politecnico di Milano, 20133 Milan, Italy. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we determine the irreducible components of the Hilbert schemes H4,g of locally Cohen-Macaulay space curves of degree four and arbitrary arithmetic genus g: there are roughly ∼(g2/24) of them, most of which are families of multiplicity structures on lines. We give deformations which show that these Hilbert schemes are connected. For g≤−3 we exhibit a component that is disjoint from the component of extremal curves and use this to give a counterexample to a conjecture of Aït-Amrane and Perrin.

Keywords

Hilbert schemes of locally Cohen–Macaulay curvesmultiplicity structures on curves
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 2 , November 2003 , pp. 169 - 196
Copyright
© 2003 Kluwer Academic Publishers