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arXiv · 0803.1208

Systems with the integer rounding property in normal monomial subrings

Luis A. Dupont·Carlos Renteria-Marquez·Rafael H. Villarreal
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Abstract

Let C be a clutter and let A be its incidence matrix. If the linear system x>=0;xA<=1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a connected graph, we describe when the aforementioned linear system has the integer rounding property in combinatorial and algebraic terms using graph theory and the theory of Rees algebras. As a consequence we show that the extended Rees algebra of the edge ideal of a bipartite graph is Gorenstein if and only if the graph is unmixed.

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Luis A. Dupont, Carlos Renteria-Marquez, Rafael H. Villarreal. 2010-04-29. Systems with the integer rounding property in normal monomial subrings. https://arxiv.org/abs/0803.1208

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