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

DOI:
https://doi.org/10.1090/S0002-9939-08-09308-8

Published electronically:
October 9, 2008

MathSciNet review:
2448558

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-08-09308-8

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