On degeneracy schemes of maps of vector bundles and applications to   holomorphic foliations
  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. 
Carolina Araujo and Maur\'icio Corr\^ea Jr
math.AG math.CV