Maurício Corrêa

On the singular scheme of split foliations

We prove that the tangent sheaf of a codimension one locally free distribution splits as a sum of line bundles if and only if its singular scheme is arithmetically Cohen-Macaulay. In addition, we show that a foliation by curves is given by an intersection of generically transversal holomorphic distributions of codimension one if and only if its singular scheme is arithmetically Buchsbaum. Finally, we establish that these foliations are determined by their singular schemes, and deduce that the Hilbert scheme of certain arithmetically Buchsbaum schemes of codimension

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

2

INEQUALITIES FOR CHARACTERISTIC NUMBERS OF FLAGS OF DISTRIBUTIONS AND FOLIATIONS

is birational to a Grassmannian.

Residues for flags of 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 foliations of arbitrary rank on

Rank two nilpotent co-Higgs sheaves on complex surfaces

\mathbb P ^n

On non-Kupka points of codimension one foliations on ℙ3

Pn to be uniquely determined by their singular schemes.

Foliations by curves with curves as singularities@@@Feuilletages par des courbes ayant des courbes comme singularités

We prove inequalities relating the degrees of holomorphic distributions and of holomorphic foliations forming a flag on . The search for such inequalities is motivated by the so-called Poincare problem for foliations and also by a question raised by M. Brunella and A. Lins Neto.

Classification of holomorphic foliations on Hopf manifolds

Abstract In this work we prove a Baum–Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum–Bott type rationality conjecture in this context.