Residues for flags of holomorphic foliations

TL;DR

This paper establishes a Baum-Bott type residue theorem for flags of holomorphic foliations, introduces Nash residues for these flags, and addresses a related rationality conjecture.

Contribution

It extends residue theory to flags of holomorphic foliations and introduces Nash residues, providing partial solutions to the Baum-Bott rationality conjecture.

Findings

Proved a Baum-Bott type residue theorem for flags of holomorphic foliations

Defined Nash residues for flags of foliations

Provided partial answers to the Baum-Bott rationality conjecture

Abstract

In this work we prove a Baum-Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum-Bott type rationality conjecture in this context .