Degree of the Exceptional Component of the Space of Holomorphic Foliations of Degree Two and Codimension One in P3

TL;DR

This paper calculates the degree of the exceptional component in the space of degree two, codimension one holomorphic foliations in P3 using explicit parameter space construction and equivariant intersection theory.

Contribution

It introduces an explicit fiber bundle parameter space and applies Bott's formula to compute the degree of the exceptional component.

Findings

Degree of the exceptional component determined

Explicit fiber bundle parameter space constructed

Degree expressed as an integral via equivariant intersection theory

Abstract

The purpose of this thesis is to obtain the degree of the exceptional component of the space of holomorphic foliations of degree two and codimension one in P3. I construct a parameter space as an explicit fiber bundle over the variety of complete flags. Using tools from equivariant intersection theory, especially Bott's formula, the degree is expressed as an integral over our parameter space.