Title

Degrees of generators of ideals defining curves in projective space

Authors

Authors

H. M. Martin; J. C. Migliore;S. Nollet

Comments

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Abbreviated Journal Title

Commun. Algebr.

Keywords

LIAISON CLASS; Mathematics

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 subscheme, 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 P-3, 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.

Journal Title

Communications in Algebra

Volume

26

Issue/Number

4

Publication Date

1-1-1998

Document Type

Article

Language

English

First Page

1209

Last Page

1231

WOS Identifier

WOS:000072700200015

ISSN

0092-7872

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