An explicit duality for quasi-homogeneous ideals

Given r≥n$r\ge n$ quasi-homogeneous polynomials in n$n$ variables, the existence of a certain duality is shown and made explicit in terms of generalized Morley forms. This result, that can be seen as a generalization of [Corollary 3.6.14, Jouanolou, J.-P., 1996. Résultant anisotrope, compléments et applications. Electron. J. Combin. 3 (2), Research Paper 2, approx. 91 pp. (electronic), the Foata Festschrift] where this duality is proved in the case r=n$r=n$, was observed by the author at the same time. We will actually closely follow the proof of the above-cited corollary in this paper.