Inequalities for characteristic numbers of flags of distributions and foliations

TL;DR

This paper establishes inequalities linking the degrees of holomorphic distributions and foliations arranged in a flag on projective space, inspired by the Poincaré problem for foliations.

Contribution

It introduces new inequalities that relate characteristic numbers of flags of distributions and foliations on projective space, extending classical results.

Findings

Derived inequalities connecting degrees of distributions and foliations.

Provided bounds inspired by the Poincaré problem.

Enhanced understanding of characteristic numbers in complex geometry.

Abstract

We prove inequalities relating the degrees of holomorphic distributions and of holomorphic foliations forming a flag on $\mathbb{P}^n$. Such inequalities are inspired by the so called Poincar\'e problem for foliations.