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.
@article{urn:eudml:doc:41250,
title = {Combinatoric of syzygies for semigroup algebras.},
journal = {Collectanea Mathematica},
volume = {49},
year = {1998},
pages = {239-256},
zbl = {0929.13007},
mrnumber = {MR1677160},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41250}
}
Briales, Emilio; Pisón, Pilar; Campillo, Antonio; Marijuán, Carlos. Combinatoric of syzygies for semigroup algebras.. Collectanea Mathematica, Tome 49 (1998) pp. 239-256. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41250/