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 1984. An explicit constructive description of these varieties has been developed in a previous paper by the same authors.
On Stanley-Reisner rings of reduction number one
BARILE, Margherita;
2000-01-01
Abstract
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 1984. An explicit constructive description of these varieties has been developed in a previous paper by the same authors.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
