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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Standard graded vertex cover algebras, cycles and leaves


Authors: Jürgen Herzog, Takayuki Hibi, Ngô Viêt Trung and Xinxian Zheng
Journal: Trans. Amer. Math. Soc. 360 (2008), 6231-6249
MSC (2000): Primary 13A30, 05C65
Published electronically: July 28, 2008
MathSciNet review: 2434285
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Abstract: The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining these algebras. It turns out that such simplicial complexes are closely related to a range of hypergraphs which generalize bipartite graphs and trees. These relationships allow us to obtain very general results on standard graded vertex cover algebras which cover previous major results on Rees algebras of squarefree monomial ideals.


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Additional Information

Jürgen Herzog
Affiliation: Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Email: juergen.herzog@uni-essen.de

Takayuki Hibi
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: hibi@math.sci.osaka-u.ac.jp

Ngô Viêt Trung
Affiliation: Institute of Mathematics, Vien Toan Hoc, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam
Email: nvtrung@math.ac.vn

Xinxian Zheng
Affiliation: Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Email: xinxian.zheng@uni-essen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04461-9
PII: S 0002-9947(08)04461-9
Received by editor(s): June 12, 2006
Published electronically: July 28, 2008
Additional Notes: The third author was supported by the ‘Leibniz-Program’ of Hélène Esnault and Eckart Viehweg during the preparation of this paper.
Article copyright: © Copyright 2008 American Mathematical Society