Seminário de Pesquisa do Departamento de Matemática

Data: Segunda-feira dia 25/04, às 11:00
Local: Sala 20 da Pós-Graduação, Instituto de Matemática/UFBA
Palestrante: Prof. Sergey Agafonov, Matemática/UFPB

(Obs: o resumo está em inglês, mas a palestra será em português)

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

A finite collection of  foliations form a web. Blaschke discovered that already for a 3-web in the plane, there is a nontrivial local invariant, namely the curvature form. Thus any local classification of 3-webs necessarily has functional moduli if no restriction on the class of
webs is imposed. The most symmetric is a hexagonal 3-web when the curvature is supposed to vanish identically. In a regular point a hexagonal 3-web is locally diffeomorphic to 3 families of parallel lines. For singular points, where at least two foliations are not transverse, two hexagonal 3-webs are not necessarily locally diffeomorphic.
We provide a complete classification of  hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions:
1)      the Chern connection form remains holomorphic at the singular point,
2)      the web admits at least one infinitesimal symmetry at this point.
As a by-product, classification of hexagonal weighted homogeneous 3-webs is obtained.