Logarithmic affine structures, parallelizable $d$-webs and normal forms

Ruben Lizarbe and Frank Loray

Vol. 319 (2022), No. 2, 371–396

DOI: 10.2140/pjm.2022.319.371

Abstract

We study the local analytic classification of affine structures with logarithmic pole on complex surfaces. With this result in hand, we can get the local classification of the logarithmic parallelizable $d$-webs, $d\ge 3$.

Keywords

affine structures, affine connections, webs, singularities, normal form

Mathematical Subject Classification

Primary: 32S65, 53A60, 53B05, 53C10

Milestones

Received: 1 December 2021

Revised: 20 March 2022

Accepted: 3 July 2022

Published: 11 September 2022