Abstract

DUPONT, Luis A.; RENTERIA-MARQUEZ, Carlos  and  VILLARREAL, Rafael H.. Systems with the integer rounding property in normal monomial subrings. An. Acad. Bras. Ciênc. [online]. 2010, vol.82, n.4, pp. 801-811. ISSN 0001-3765.  http://dx.doi.org/10.1590/S0001-37652010000400002.

Let C be a clutter and let A be its incidence matrix. If the linear system x > 0; x A < 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.

Keywords : canonical module; a-invariant; normal ideal; perfect graph; maximal cliques; Rees algebra; Ehrhart ring; integer rounding property.