Combinatorics of syzygies for semigroup algebras

• Autores: Emilio Briales Morales , Antonio Campillo López , Carlos Marijuán López , Pilar Pisón Casares
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 2-3, 1998, págs. 239-256
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.

• Referencias bibliográficas
  • A. Aramova and J. Herzog, Free resolutions and Koszul homology, J. Pure Appl. Algebra 105(1) (1995), 1–16.
  • H. Bresinsky, Binomial generating sets for monomial curves, with applications in $A^4$, Rend. Sem. Mat. Univ. Politec. Torino 46(3) (1988),...
  • E. Briales, A. Campillo, C. Marijuán and P. Pisón, Minimal Systems of Generators for Ideals of Semigroups, J. Pure Appl. Algebra 127 (1998),...
  • A. Campillo and Ph. Giménez, Syzygies of affine toric varieties, Preprint Universidad de Valladolid, January 1997.
  • A. Campillo and C. Marijuán, Higher relations for a numerical semigroup, Sém. Théor. Nombres Bordeaux 3 (1991), 249–260.
  • A. Campillo and P. Pisón, Generators of a monomial curve and graphs for the associated semigroup, Bull. Soc. Math. Belg. Sér. A 45(1-2) (1993),...
  • A. Campillo and P. Pisón, L’idéal d’un semi-groupe de type fini, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 1303–1306.
  • M.P. Cavaliere and G. Niesi, On monomial curves and Cohen-Macaulay type, Manuscripta Math. 42(2-3) (1983), 147–159.
  • S. Eliahou, Courbes monomiales et algèbre de Rees symbolique, Doctoral thesis 2080, Université of Genève, 1983.
  • J. Herzog, Generators and Relations of Semigroups and Semigroup Rings, Manuscripta Math. 3 (1970), 175–193.
  • Y. Kamoi, Defining ideals of Cohen-Macaulay semigroups rings, Comm. Algebra 20 (1992), 3163–3189.
  • E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Amer. Math. Soc. 25 (1970), 748–751.
  • P. Pisón, Métodos combinatorios en Álgebra local y Curvas monomiales en dimensión 4, Doctoral thesis, Universidad de Sevilla, 1991.
  • J.C. Rosales, An algorithmic method to compute a minimal relation for any numerical semigroup, Internat. J. Algebra Comput. 6(4) (1996), 441–455.
  • U. Schäfer and P. Schenzel, Dualing complexes of affine semigroup rings, Trans. Amer. Math. Soc. 322 (1990), 561–582.
  • B. Sturmfels, Grobner Bases and Convex Polytopes, American Mathematical Society, University Lecture Series, Vol. 8, Providence, RI, 1995.
  • N.V. Trung and L.T. Hoa, Affine semigroups and Cohen-Macaulay rings generated by monomials, Trans. Amer. Math. Soc. 298 (1986), 145–167.