Poincaré problem for weighted projective foliations

Foliations on Complex Projective Surfaces

In this text we shall review the classification of foliations on complex projective surfaces according to their Kodaira dimension, following McQuillan’s seminal paper [MQ1] with some complements and variations given by [Br1] and [Br2]. Most of the proofs will be only sketched, and the text should be considered as guidelines to the above works (and related ones), with no exhaustivity nor selfcon...

Projective varieties invariant by one - dimensional foliations

This work concerns the problem of relating characteristic numbers of onedimensional holomorphic foliations of PC to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional holomorphic foliation F of M is a morphism Φ : L −→ TM where L is a holomorphic line bundle on M . The singular set of F is the analytic subvariety sing(F) = {p ...

On holomorphic foliations with projective transverse structure

We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of th...

Solvability for Parabolic Poincaré Problem

Weighted Projective Varieties

0. Introduction i. Weighted projective space i.i. Notations 1.2. Interpretations 1.3. The first properties 1.4. Cohomology of 0F(n) 1.5. Pathologies 2. Bott's theorem 2.1. The sheaves ~(n) 2.2. Justifications 2.3. Cohomology of ~$(n) 3. Weighted complete intersections 3.1. Quasicones 3.2. Complete intersections 3.3. The dualizing sheaf 3.4. The Poincare series 3.5. Examples 4. The Hodge structu...