Brunella-Khanedani-Suwa variational residues for invariant currents

TL;DR

This paper establishes a variational residue theorem for invariant currents in holomorphic foliations, providing new conditions under which leaves accumulate at intersections of singular sets and invariant currents.

Contribution

It introduces a novel residue theorem for invariant currents in holomorphic foliations, extending previous results to singular cases.

Findings

Proves a Brunella-Khanedani-Suwa type residue theorem for invariant currents.

Provides conditions for leaf accumulation at singular set intersections.

Enhances understanding of the dynamics of holomorphic foliations.

Abstract

In this work we prove a Brunella-Khanedani-Suwa variational type residue theorem for currents invariant by holomorphic foliations. As a consequence, we give conditions for the leaves of a singular holomorphic foliation to accumulate in the intersection of the singular set of the foliation with the support of an invariant current.