Degrees of generators of ideals defining curves in projective space

    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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