Joseph P. Brennan, Luis A. Dupont and Rafael H. Villarreal: Duality, a-invariants and canonical modules of rings arising from linear optimization problems, p.279-305

Abstract:

The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial ideals and monomial subrings. We study the normality and Gorenstein property--as well as the canonical module and the $a$-invariant--of Rees algebras and subrings arising from systems with the integer rounding property. We relate the algebraic properties of Rees algebras and monomial subrings with integer rounding properties and present a duality theorem.

Key Words: $a$-invariant, canonical module, Gorenstein ring, normal subring, integer rounding property, Rees algebra, Ehrhart ring, bipartite graph, max-flow min-cut, clutter.

2000 Mathematics Subject Classification: Primary: 13H10,
Secondary: 13F20, 13B22, 52B20

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