On the Gorensteinness of broken circuit complexes and Orlik-Terao ideals

Autor(en): Van Le, Dinh
Stichwörter: ALGEBRAS; Broken circuit complex; Complete intersection; Gorenstein; Hyperplane arrangement; Mathematics; Matroid; Orlik-Terao algebra
Erscheinungsdatum: 2014
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF COMBINATORIAL THEORY SERIES A
Volumen: 123
Ausgabe: 1
Startseite: 169
Seitenende: 185
Zusammenfassung: 
It is proved that the broken circuit complex of an ordered matroid is Gorenstein if and only if it is a complete intersection. Several characterizations for a matroid that admits such an order are then given, with particular interest in the h-vector of broken circuit complexes of the matroid. As an application, we prove that the Orlik Terao algebra of a hyperplane arrangement is Gorenstein if and only if it is a complete intersection. Interestingly, our result shows that the complete intersection property (and hence the Gorensteinness as well) of the Orlik Terao algebra can be determined from the last two nonzero entries of its h-Vector. (C) 2013 Elsevier Inc. All rights reserved.
ISSN: 00973165
DOI: 10.1016/j.jcta.2013.12.007

Show full item record

Google ScholarTM

Check

Altmetric