Title

Degrees of generators of ideals defining curves in projective space

Abstract

For an arithmetically Cohen-Macaulay subscheme of projective space, there is a well-known bound for the highest degree of a minimal generator for the defining ideal of the subschema, in terms of the Hilbert function. We prove a natural extension of this bound for arbitrary locally Cohen-Macaulay subschemes. We then specialize to curves in P3, and show that the curves whose defining ideals have generators of maximal degree satisfy an interesting cohomological property. The even liaison classes possessing such curves are characterized, and we show that within an even liaison class, all curves with the property satisfy a strong Lazarsfeld-Rao structure theorem. This allows us to give relatively complete conditions for when a liaison class contains curves whose ideals have maximal degree generators, and where within the liaison class they occur. Copyright © 1998 by Marcel Dekker, Inc.

Publication Date

1-1-1998

Publication Title

Communications in Algebra

Volume

26

Issue

4

Number of Pages

1209-1231

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/00927879808826194

Socpus ID

26444591104 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/26444591104

This document is currently not available here.

Share

COinS