Local classification of singular hexagonal 3-webs with holomorphic Chern connection and infinitesimal symmetries

TL;DR

This paper classifies singular hexagonal 3-web germs in the complex plane that have holomorphic Chern connections and infinitesimal symmetries, also providing a classification for weighted homogeneous cases.

Contribution

It offers a complete classification of such webs under specified conditions, advancing understanding of their local structure and symmetries.

Findings

Classification of singular hexagonal 3-web germs with holomorphic Chern connection

Identification of webs admitting infinitesimal symmetries

Classification of weighted homogeneous 3-webs

Abstract

We provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection remains holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained.