Infinitesimal symmetries for implicit planar webs

TL;DR

This paper explores the geometric properties of implicit planar webs generated by differential equations, focusing on their infinitesimal symmetries using advanced meromorphic connection techniques.

Contribution

It introduces a novel approach to analyze infinitesimal symmetries of planar webs via meromorphic connections in the complex setting.

Findings

Characterization of symmetries using meromorphic connections

Application to algebraic and analytic differential equations

Enhanced understanding of web geometry in complex analysis

Abstract

In the complex setting, let $F(x,y,y')=0$ be an analytic or algebraic differential equation with $y'$-degree $d$. We deal with the qualitative study of such equations through the geometry of the planar $d$-web generated by the generic family of integral curves. Infinitesimal symmetries of these configurations are discussed by using meromorphic connections methods "\`a la Cartan-Spencer".