New Ideas for Resolution of Singularities in Arbitrary Characteristics

2010/04/30 by Tohsuke Urabe, Urabe, Tohsuke
Engineering · Mathematics · #14E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1004.5446

openalex publication_date 2010/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The concept of the maximal contact is the key in Hironaka's resolution theory. It treats local theory, and it is not effective in positive characteristics. This is the essential reason why Hironaka's theory treats only the case of characteristic zero. In this article we propose the substitute for the maximal contact, which is effective in any characteristics of the ground field. We replace the maximal contact by a theorem in the theory of torus embeddings. Using essential ideas here, we would like to establish the theory of resolution of singularities in arbitrary characteristics in a global sense in the forthcoming articles.

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