Transversely affine foliations on projective manifolds

TL;DR

This paper characterizes the structure of singular transversely affine foliations of codimension one on projective manifolds with zero first Betti number, linking it to flat meromorphic connections.

Contribution

It provides a new structural theorem for such foliations, connecting geometric foliations to algebraic flat connections.

Findings

Structure theorem for singular transversely affine foliations

Connection to rank two reducible flat meromorphic connections

Applicable to projective manifolds with zero first Betti number

Abstract

We describe the structure of singular transversely affine foliations of codimension one on projective manifolds X with zero first Betti number. Our result can be rephrased as a theorem on rank two reducible flat meromorphic connections.