Degree of the Exceptional Component of the Space of Holomorphic Foliations of Degree Two and Codimension One in P^3

Abstract

The purpose of this work is to obtain the degree of the exceptional component, (...), of the space of holomorphic foliations of degree two and codimension one in (...). As shown in the celebrated work by Dominique Cerveau and Alcides Lins Neto [13], E(3) is a 13-dimensional component. It is the closure of the orbit under the natural action of (...) of the foliation defined by the differential form (...). Our first task is to unravel a geometric characterization of the pair g; f. This leads us to the construction of a parameter space as an explicit fiber bundle over the variety of complete ags. Using tools from equivariant intersection theory, especially Bott's formula, the degree is expressed as an integral over our parameter space.