Monomial ideals and the Gorenstein liaison class of a complete intersection

J. Migliore, U. Nagel

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

In an earlier work, the authors described a mechanism for lifting monomial ideals to reduced unions of linear varieties. When the monomial ideal is Cohen-Macaulay (including Artinian), the corresponding union of linear varieties is arithmetically Cohen-Macaulay. The first main result of this paper is that if the monomial ideal is Artinian then the corresponding union is in the Gorenstein linkage class of a complete intersection (glicci). This technique has some interesting consequences. For instance, given any (d + 1)-times differentiable O-sequence H, there is a nondegenerate arithmetically Cohen-Macaulay reduced union of linear varieties with Hilbert function H which is glicci. In other words, any Hilbert function that occurs for arithmetically Cohen-Macaulay schemes in fact occurs among the glicci schemes. This is not true for licci schemes. Modifying our technique, the second main result is that any Cohen-Macaulay Borel-fixed monomial ideal is glicci. As a consequence, all arithmetically Cohen-Macaulay subschemes of projective space are glicci up to flat deformation.

Original languageEnglish
Pages (from-to)25-36
Number of pages12
JournalCompositio Mathematica
Volume133
Issue number1
DOIs
StatePublished - 2002

Keywords

  • Artinian
  • Borel-fixed
  • Complete intersection
  • Glicci
  • Gorenstein liaison
  • Hilbert function
  • Liaison
  • Licci
  • Lifting
  • Linkage
  • Monomial ideal

ASJC Scopus subject areas

  • Algebra and Number Theory

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