Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 1, pp. 141150 (2007) 

A note on Rees algebras and the MFMC propertyIsidoro Gitler, Carlos E. Valencia and Rafael H. VillarrealDepartamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14740, 07000 México City, D.F., email: vila@math.cinvestav.mxAbstract: We study irreducible representations of Rees cones and characterize the maxflow mincut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and commutative algebra. As a byproduct we obtain an effective method, based on the program Normaliz\/ [B], to determine whether a given clutter satisfies the maxflow mincut property. Let $\cal C$ be a clutter and let $I$ be its edge ideal. We prove that $\cal C$ has the maxflow mincut property if and only if $I$ is normally torsion free, that is, $I^i=I^{(i)}$ for all $i\geq 1$, where $I^{(i)}$ is the $i$th symbolic power of $I$. [B] Bruns, W.; Koch, R.: Normaliz  a program for computing normalizations of affine semigroups. 1998. Available via anonymous ftp from ftp.mathematik.UniOsnabrueck.DE/pub/osm/kommalg/software Full text of the article:
Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.
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