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Rees cones and monomial rings of matroids

Rafael H. Villarreal
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Abstract

Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid (or a polymatroid) and study their facets. Some applications to Rees algebras are presented. It is shown that the basis monomial ideal of a matroid (or a polymatroid) is normal.

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Rafael H. Villarreal. 2011-04-03. Rees cones and monomial rings of matroids. https://arxiv.org/abs/math/0601520

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