Resumen de Combinatorics of syzygies for semigroup algebras

Emilio Briales Morales, Antonio Campillo López, Carlos Marijuán López, Pilar Pisón Casares

• We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen- Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.