Formes d'inertie et complexe de Koszul associ\'es \`a des polyn\^omes plurihomog\`enes

TL;DR

This paper explores the algebraic structures related to common zeros of multihomogeneous polynomials, focusing on inertial forms, Koszul complexes, and Cech cohomology, establishing analogues of classical theorems in this context.

Contribution

It introduces new algebraic results connecting inertial forms, Koszul complexes, and cohomology, including analogues of Hurwitz and McCoy theorems for multihomogeneous polynomials.

Findings

Established an analogue of Hurwitz theorem for multihomogeneous polynomials.

Derived a McCoy-type theorem in a specific case of the studied algebraic structures.

Clarified the role of Koszul and Cech cohomology in the theory of common zeros.

Abstract

The eThe existence of common zero of a family of polynomials has led to study of inertial forms whose homogeneous part of degree 0 constitutes the ideal resultant. The Koszul anc Cech cohomology groups play a fundamental role in this study. An analogueous of Hurwitz theorem is given and also we finds a MCoy theorem in a particular case of this study.