On Stanley-Reisner rings of reduction number one

• Marguerita Barile ^[1] ; Marcel Morales ^[2]
  1. [1] University of Bari Aldo Moro

     University of Bari Aldo Moro

     Bari, Italia

     
  2. [2] Universite de Grenoble I
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 29, Nº 3, 2000, págs. 605-610
• Idioma: inglés
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• Resumen

  • In this paper we study a particular class of algebraic varieties, which are the finite unions of linear spaces. For a suitable choice of the system of coordinates these varieties are defined by squarefree monomials. Their coordinate rings are Stanley-Reisner rings of simplicial complexes. Each simplicial complex determines a simple, one-dimensional non directed graph. We give a combinatorial criterion on the graph which assures that the Stanley-Reisner ring has a system of parameters consisting of linear forms. The resulting class of Stanley-Reisner rings strictly includes those which are Cohen-Macaulay of minimal degree. These belong to the class of varieties classified by Eisenbud and Goto in [2]. An explicit constructive description of these varieties has been developed in [ 1 ] .