Why (a,b)-modules, frescos and themes ?

TL;DR

This paper advocates for using (a,b)-modules, a simple algebraic tool, to study complex singularities, providing an elementary overview of their application in analyzing holomorphic function singularities.

Contribution

It introduces (a,b)-modules as an effective algebraic framework for singularity analysis, highlighting their simplicity and utility.

Findings

(a,b)-modules effectively analyze singularities.

Provides an elementary overview of (a,b)-modules.

Supports the adoption of (a,b)-modules in singularity theory.

Abstract

This text is an advocacy for the use of (a,b)-modules (formal Brieskorn modules) in the study of the singularity of a holomorphic function on a complex manifold. It gives a short an elementary overview on this simple algebraic tool.