Foliations on the projective plane with finite group of symmetries

Dynamics of Singular Holomorphic Foliations on the Complex Projective Plane

This manuscript is a revised version of my Master’s thesis which was originally written in 1992 and was presented to the Mathematics Department of University of Tehran. My initial goal was to give, in a language accessible to non-experts, highlights of the 1978 influential paper of Il’yashenko on singular holomorphic foliations on CP [I3], providing short, self-contained proofs. Parts of the ex...

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...

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...

Group Actions on Vector Bundles on the Projective Plane

We study the action of the group of automorphisms of the projective plane on the Maruyama scheme of sheaves MP 2(r, c1,c2) of rank r and Chern classes c1 = 0 and c2 = n and obtain sufficient conditions for unstability in the sense of Mumford’s geometric invariant theory. The conditions are in terms of the splitting behaviour of sheaves when restricted to lines in the projective plane. A very st...

Group of Homography in Real Projective Plane