Marcio G. Soares

Singularities of logarithmic foliations

A logarithmic 1-form on

On the geometry of Poincaré's problem for one-dimensional projective foliations

\mathbb C\mathbb P^n

INEQUALITIES FOR CHARACTERISTIC NUMBERS OF FLAGS OF DISTRIBUTIONS AND FOLIATIONS

can be written as \omega=\biggl(\prod_0^m F_j\biggr)\sum_0^m \lambda_i\frac{dF_i}{F_i}=\lambda_0 \widehat F_0 \,dF_0+\cdots+\lambda_m \widehat F_m \,dF_m with

A note on Poincaré’s problem for quasi-homogeneous foliations

\widehat F_i=(\prod_0^m F_j)/F_i

A Bott-Type Residue Formula on Complex Orbifolds

for some homogeneous polynomials F i of degree d i and constants

Hypersurfaces invariant by Pfaff systems

\lambda_i\in{\mathbb C}^\star

On the index of a holomorphic vector field tangent to a singular variety

such that

The Poincaré problem for hypersurfaces invariant by one-dimensional foliations

\sum\lambda_id_i=0

LOCAL BRUNELLA'S ALTERNATIVE I. RICH FOLIATIONS

. For general

Algebraic integrability of polynomial differential r-forms

F_i,\lambda_i