2018/12/01 by Augusto Nóbile, Nobile, Augusto · 1 citation
Mathematics · #14B05 #14B07 #14E15 #14E18 #14E99 #14J99 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1812.00288
openalex publication_date 2018/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper seeks to prove the bijectivity of the "Nash mapping" from the set of irreducible components of the scheme parametrizing analytic arcs on an algebraic surface X whose origin is a singular point, into the set of irreducible components of the exceptional locus of a minimal desingularization X' of X when the base field has positive characteristic. The idea is to view the surface as a specialization of another defined over a field of characteristic zero. A number of related results are proved. Among them, the construction of a scheme of arcs for a suitable one parameter family of surfaces which, by using a theorem of M. Artin on lifting of normal surface singularities to characteristic zero, seems a reasonable candidate to be the desired tool. But there are some points, necessary for a complete proof, which are not verified yet.