Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T04:19:05.732Z Has data issue: false hasContentIssue false

Hilbert Schemes of Degree Four Curves

Published online by Cambridge University Press:  04 December 2007

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.

Type
Research Article
Copyright
© 2003 Kluwer Academic Publishers