Local classification of singular hexagonal 3-webs with holomorphic Chern   connection and infinitesimal symmetries
  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. 
Sergey Agafonov
math.DG math.CV