The Nash problem from a geometric and topological perspective

2018/05/03 by Javier Fernández de Bobadilla, de Bobadilla, Javier Fernández, María Pe Pereira +1
Mathematics · #14B05 #14J17 #32S05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1805.01418

openalex publication_date 2018/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later we summarize the main ideas in the higher dimensional statement and proof by de Fernex and Docampo. We end the paper by explaining later developments on generalized Nash problem and on Kollár and Nemethi's study about holomorphic arcs.

Related

• The embedded Nash problem in singular spaces: the case of surfaces
• Nash problem for surface singularities is a topological problem
• Three-dimensional counter-examples to the Nash problem
• The Nash problem of arcs and the rational double point E₆
• Résolution du problème des arcs de Nash pour une famille d'hypersurfaces quasi-rationnelles