Limits of tangent spaces to definable sets

2020/10/07 by Sĩ Tiệp Đinh, Dinh, Si Tiep, Olivier Le Gal +3
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2010.03445

openalex publication_date 2020/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the set of tangent limits at a given point to a set definable in any o-minimal structure by characterizing the set of exceptional rays in the tangent cone to the set at that point and investigating the set of tangent limits along these rays. Several criteria for determining exceptional rays will be given. The main results of the paper generalize, to the o-minimal setting and to arbitrary dimension, the main results of O'Shea--Wilson which deals with algebraic surfaces in \mathbb R³.

Citations

• Geometric categories and o-minimal structures

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