Glicci ideals

Juan Migliore, Uwe Nagel

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A central problem in liaison theory is to decide whether every arithmetically Cohen-Macaulay subscheme of projective n-space can be linked by a finite number of arithmetically Gorenstein schemes to a complete intersection. We show that this can indeed be achieved if the given scheme is also generically Gorenstein and we allow the links to take place in an (n+ 1)-dimensional projective space. For example, this result applies to all reduced arithmetically Cohen-Macaulay subschemes. We also show that every union of fat points in projective 3-space can be linked in the same space to a union of simple points in finitely many steps, and hence to a complete intersection in projective 4-space.

Original languageEnglish
Pages (from-to)1583-1591
Number of pages9
JournalCompositio Mathematica
Volume149
Issue number9
DOIs
StatePublished - Sep 2013

Keywords

  • Gorenstein subscheme
  • arithmetically Cohen-Macaulay subscheme
  • fat points
  • glicci
  • liaison
  • linkage
  • reduced scheme

ASJC Scopus subject areas

  • Algebra and Number Theory

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