Logarithmic affine structures, parallelizable d-webs and normal forms

TL;DR

This paper classifies affine structures with logarithmic poles on complex surfaces and applies these results to classify logarithmic parallelizable d-webs for d ≥ 3, advancing understanding of their local analytic forms.

Contribution

It provides a new local classification framework for affine structures with logarithmic poles and applies it to classify logarithmic parallelizable webs.

Findings

Classification of affine structures with logarithmic poles on complex surfaces.

Local classification of logarithmic parallelizable d-webs for d ≥ 3.

Development of normal forms for these structures.

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.