Note sur le lieu discriminant d'une hypersurface de bi-degr\'e $(m, n).$

TL;DR

This paper introduces a novel topological approach using groupoids to analyze the discriminantal loci of algebraic varieties, specifically hypersurfaces of bi-degree (m, n), in product spaces.

Contribution

It develops a new topological method leveraging groupoids to study discriminantal loci, providing a fresh perspective on the monodromy of such varieties.

Findings

Effective description of monodromy using groupoids

Application to hypersurfaces of bi-degree (m, n)

Enhanced understanding of discriminantal loci topology

Abstract

We present a new topological method to study the discriminantal loci of an algebraic variety defined in a product of projective spaces. Our approach relies on an efficient use of groupoid to describe the monodromy. As an example, we treat here the discriminantal loci of an hypersurface of bi-degree $(m, n).$