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
Copyright Status
Unknown
Socpus ID
26444591104 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/26444591104
STARS Citation
Martin, Heath M.; Migliore, Juan C.; and Nollet, Scott, "Degrees of generators of ideals defining curves in projective space" (1998). Scopus Export 1990s. 3219.
https://stars.library.ucf.edu/scopus1990/3219