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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Vertex cover algebras of unimodular hypergraphs


Authors: Jürgen Herzog, Takayuki Hibi and Ngô Viêt Trung
Journal: Proc. Amer. Math. Soc. 137 (2009), 409-414
MSC (2000): Primary 13D02, 05C65
Published electronically: October 9, 2008
MathSciNet review: 2448558
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Abstract: It is proved that all vertex cover algebras of a hypergraph are standard graded if and only if the hypergraph is unimodular. This has interesting consequences on the symbolic powers of 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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09308-8
PII: S 0002-9939(08)09308-8
Keywords: Vertex cover algebra, unimodular hypergraph, symbolic power, monomial ideal
Received by editor(s): March 18, 2007
Published electronically: October 9, 2008
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2008 American Mathematical Society