Transversely affine holomorphic foliations of arbitrary codimension - I

TL;DR

This paper investigates holomorphic foliations with affine transverse structures, providing a characterization via differential forms and extending results to singular cases, advancing understanding of their geometric properties.

Contribution

It introduces a new characterization of transversely affine foliations using matrix-valued differential forms and extends the theory to singular foliations.

Findings

Characterization of transversely affine foliations via differential forms

Extension theorem for foliations with singularities

Framework for studying singular holomorphic foliations

Abstract

We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally to the study of the case of foliations with singularities. A first extension theorem is then proved in the generic singularities framework.