Baum-Bott residue of flags of holomorphic distributions

TL;DR

This paper extends Baum-Bott residue theory to flags of holomorphic distributions, providing a method to compute residues and relating degrees, tangency, Euler characteristic, and curve degree in projective space.

Contribution

It introduces an extension of residue theory to flags of holomorphic distributions and offers an effective computational approach for specific cases.

Findings

Residue theory extended to flags of distributions

Derived relations between degrees, tangency, and Euler characteristic

Applied results to distributions on projective space 

Abstract

In this work we extend the residue theory from flag of holomorphic foliations to flag of holomorphic distributions and we provide an effective way to calculate this class in certain cases. As a consequence, we show that if we consider a flag $\mathcal{F} = (\mathcal{F}_{1}, \mathcal{F}_{2})$ of holomorphic distributions on $\mathbb{P}^{3}$, we get a relation between the degrees of the distributions in the flag, the tangency order of distributions, the Euler characteristic and the degree of the curve $C.$