Strongly inessential elements of a perfect height 2 ideal

TL;DR

This paper investigates the presence of strongly inessential generators in perfect height 2 ideals with maximal generators, expanding on previous work about inessential elements in homogeneous ideals.

Contribution

It extends the analysis of strongly inessential generators to perfect height 2 ideals with the maximum number of generators, based on Dubreil's inequality.

Findings

Strongly inessential elements are more prevalent in certain perfect height 2 ideals.

The paper characterizes conditions under which these elements appear.

Provides new insights into the structure of saturated homogeneous ideals.

Abstract

In this paper we expand on some results exposed in a previous one, in which we introduced the concept of inessential and strongly inessential generators in a standard basis of a saturated homogeneous ideal. The appearance of strongly inessential elements seemed to be a non generic situation; in this paper we analyze their presence in a perfect height 2 ideal with the greatest number of generators, according to Dubreil's inequality.