Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals

• Autores: Luis A. Dupont, Rafael H. Villarreal
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 106, Nº 1, 2010, págs. 88-98
• Idioma: inglés
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• Resumen

  • The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let G be the comparability graph of a finite poset. If cl(G) is the clutter of maximal cliques of G, we prove that cl(G) satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.