Regularity, depth and arithmetic rank of bipartite edge ideals

被引：59

作者：

Kummini, Manoj ^{[1
]}

机构：

[1] Purdue Univ, Lafayette, IN 47907 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2009年 / 30卷 / 04期

关键词：

Monomial ideals; Graded free resolutions; Arithmetic rank;

D O I：

10.1007/s10801-009-0171-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study minimal free resolutions of edge ideals of bipartite graphs. We associate a directed graph to a bipartite graph whose edge ideal is unmixed, and give expressions for the regularity and the depth of the edge ideal in terms of invariants of the directed graph. For some classes of unmixed edge ideals, we show that the arithmetic rank of the ideal equals projective dimension of its quotient.

引用

页码：429 / 445

页数：17

共 19 条

[1] On the number of equations defining certain varieties [J].