Global stucture of webs in codimension one

TL;DR

This paper investigates the global structure and singularities of holomorphic webs in codimension one, introducing new concepts and establishing conditions under which webs are algebraic based on their caustic and other properties.

Contribution

It introduces concepts like type, reducibility, quasi-smoothness, and dicriticity, and shows algebraicity of webs can be deduced from their caustic under certain conditions.

Findings

Algebraicity of webs can be inferred from caustic properties.

Introduction of new concepts such as type, reducibility, and dicriticity.

Web properties like quasi-smoothness relate to their global structure.

Abstract

We describe the global structure of holomorphic webs in codimension one, and in particular their singularity (caustic). Various concepts are introduced, which have no interest locally near a regular point, such as the type, the reducibility, the quasi-smoothness, the CI property (complete intersection), the dicriticity... We prove for instance that the algebraicity of a web globally defined on a complex projective space may be readen on its caustic (dicriticity), at least if each irreducible component is CI, and the web quasi-smooth. .