Reduction of Singularities of Three-Dimensional Line Foliations

2010/09/07 by Felipe Cano, Cano, Felipe, Claude André Roche +3
Computer Science · Mathematics · #14B05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.1009.1348

openalex publication_date 2010/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a birational reduction of singularities for one dimensional foliations in ambient spaces of dimension three. To do this, we first prove the existence of a Local Uniformization in the sense of Zariski. The reduction of singularities is then obtained by a gluing procedure for Local Uniformization similar to Zariski's one, using an axiomatization of Zariski's work by Olivier Piltant.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Related

• Local Uniformization of Codimension One Foliations
• Resolution of 1-foliations singularities on surfaces and threefolds
• Codimension one foliations with trivial canonical class on singular spaces II
• Global dynamics and perspectives on singularities of holomorphic foliations
• Resolution of singularities of an idealistic filtration in dimension 3 after Benito-Villamayor