An explicit duality for quasi-homogeneous ideals

TL;DR

This paper establishes and explicitly describes a duality for quasi-homogeneous ideals generated by r>=n polynomials in n variables, extending previous results to a broader case.

Contribution

It generalizes a known duality from the case r=n to r>=n using generalized Morley forms, providing explicit formulas.

Findings

Proves a duality for quasi-homogeneous ideals with r>=n.

Expresses the duality explicitly via generalized Morley forms.

Extends previous duality results to more general cases.

Abstract

Given r>=n quasi-homogeneous polynomials in n variables, the existence of a certain duality is shown and explicited in terms of generalized Morley forms. This result, that can be seen as a generalization of [3,corollary 3.6.1.4] (where this duality is proved in the case r=n), was observed by the author at the same time. We will actually closely follow the proof of (loc. cit.) in this paper.