Glicci simplicial complexes

Autor(en): Nagel, Uwe
Roemer, Tim 
Stichwörter: GORENSTEIN LIAISON; IDEALS; Mathematics; Mathematics, Applied
Erscheinungsdatum: 2008
Herausgeber: ELSEVIER
Journal: JOURNAL OF PURE AND APPLIED ALGEBRA
Volumen: 212
Ausgabe: 10
Startseite: 2250
Seitenende: 2258
Zusammenfassung: 
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. (c) 2008 Elsevier B.V. All rights reserved.
ISSN: 00224049
DOI: 10.1016/j.jpaa.2008.03.005

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