2023/04/13 by Lev Birbrair, Rodrigo E. Mendes, Birbrair, Lev +1
Mathematics · #03C64 #14P15 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical and Theoretical Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2304.06610
openalex publication_date 2023/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study Multi-K-equivalence of multi-germs of functions on the plane, definable in a polynomially bounded o-minimal structure. We partition the germ of the plane at origin into zones of arcs in such a way that it produces a non-Archimedean space (set of orders and width functions) compatible with a given multigerm, encoding its asymptotic behaviour. Such a partition is called Multipizza. We show the existence, uniqueness and complete invariance of Multipizzas with respect to the Multi-K-Lipschitz equivalence.