On degeneracy schemes of maps of vector bundles and applications to holomorphic foliations

TL;DR

This paper establishes conditions under which maps of vector bundles and holomorphic distributions are uniquely determined by their degeneracy and singular schemes, with applications to projective spaces.

Contribution

It introduces new criteria for the uniqueness of vector bundle maps and holomorphic distributions based on their degeneracy and singular schemes.

Findings

Conditions for uniqueness of vector bundle maps from degeneracy schemes

Criteria for distributions on projective spaces to be determined by singular schemes

Applications to holomorphic foliations and distributions

Abstract

In this paper we provide sufficient conditions for maps of vector bundles on smooth projective varieties to be uniquely determined by their degeneracy schemes. We then specialize to holomorphic distributions and foliations. In particular, we provide sufficient conditions for distributions of arbitrary rank on projective spaces to be uniquely determined by their singular schemes.