Characteristic Numbers and invariant subvarieties for Projective Webs

TL;DR

This paper introduces characteristic numbers for holomorphic distributions on projective space, explores their relation to invariant subvarieties, and applies these concepts to bound the degree of smooth invariant hypersurfaces.

Contribution

It defines characteristic numbers for holomorphic distributions and establishes their relations to invariant subvarieties, providing bounds on invariant hypersurface degrees.

Findings

Defined characteristic numbers for holomorphic distributions.

Established relations between characteristic numbers and invariant subvarieties.

Bounded the degree of smooth invariant hypersurfaces.

Abstract

We define the characteristic numbers of a holomorphic k-distribution of any dimension on $mathbb P^n$ and obtain relations between these numbers and the characteristic numbers of an invariant subvariety. As an application we bound the degree of a smooth invariant hypersurface.