Glicci simplicial complexes

Uwe Nagel, Tim Römer

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

This note is a case study for the potential of liaison-theoretic methods to applications in Combinatorics. One of the main open questions in liaison theory is whether every homogeneous Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for Stanley-Reisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Gorenstein complexes respectively. Moreover, we construct a simplicial complex which shows that the property of being glicci depends on the characteristic of the base field. As an application of our methods we establish new evidence for two conjectures of Stanley on partitionable complexes and Stanley decompositions.

Original languageEnglish
Pages (from-to)2250-2258
Number of pages9
JournalJournal of Pure and Applied Algebra
Volume212
Issue number10
DOIs
StatePublished - Oct 2008

Bibliographical note

Funding Information:
Part of the work for this paper was done while the first author was sponsored by the National Security Agency under Grant Number H98230-07-1-0065 and by the Institute for Mathematics & its Applications, University of Minnesota, Minneapolis, MN 55455, USA.

ASJC Scopus subject areas

  • Algebra and Number Theory

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