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Standard graded vertex cover algebras, cycles and leaves
Author(s):
Jürgen
Herzog;
Takayuki
Hibi;
Ngô
Viêt
Trung;
Xinxian
Zheng
Journal:
Trans. Amer. Math. Soc.
360
(2008),
6231-6249.
MSC (2000):
Primary 13A30, 05C65
Posted:
July 28, 2008
MathSciNet review:
2434285
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Additional information
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:
10.1090/S0002-9947-08-04461-9
PII:
S 0002-9947(08)04461-9
Received by editor(s):
June 12, 2006
Posted:
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.
Copyright of article:
Copyright
2008,
American Mathematical Society
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