Degree of the exceptional component of foliations in P3

2018/06/13 by Artur Afonso Guedes Rossini, Rossini, Artur, Israel Vainsencher +1
Mathematics · #14N10 #14N15 (Primary) #37F75 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1806.04814

openalex publication_date 2018/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 P³. We 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.

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