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Castelnuovo-Mumford regularity of products of ideals.

Aldo Conca, Jürgen Herzog (2003)

Collectanea Mathematica

The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...

Combinatoric of syzygies for semigroup algebras.

Emilio Briales, Pilar Pisón, Antonio Campillo, Carlos Marijuán (1998)

Collectanea Mathematica

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.

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