Gröbner Flags and Gorenstein Algebras
Gröbner Flags and Gorenstein Algebras
复制标题
Gröbner 标志和 Gorenstein 代数
作者：
A. Conca;M. Rossi;G. Valla
本文主要研究了典型曲线、有限点集和具有低次柱脚的Artin Gorenstein代数等经典簇和代数的二次曲面的Koszul性质和具有Gröbner基的性质。我们的方法是基于Gröbner标志和Koszul过滤的概念。主要结果是：当标准曲线的理想由二次曲面定义时，它的二次曲面的Gröbner基的存在性，Pn中一般线性位置上s ≤ 2n个点的定义理想的二次曲面的Gröbner基的存在性，以及柱脚度为3的“一般”Artin Gorenstein代数的Koszul性质。
The goal of this paper is to study the Koszul property and the property of having a Gröbner basis of quadrics for classical varieties and algebras as canonical curves, finite sets of points and Artinian Gorenstein algebras with socle in low degree. Our approach is based on the notion of Gröbner flags and Koszul filtrations. The main results are the existence of a Gröbner basis of quadrics for the ideal of the canonical curve whenever it is defined by quadrics, the existence of a Gröbner basis of quadrics for the defining ideal of s ≤ 2n points in general linear position in Pn, and the Koszul property of the ‘generic’ Artinian Gorenstein algebra of socle degree 3.