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Moscow Mathematical Journal

Volume 22, Issue 3, July–September 2022  pp. 521–560.

Combinatorial Monomialization for Generalized Real Analytic Functions in Three Variables

Authors:  Jesús Palma-Márquez (1)
Author institution:(1) Instituto de Matemáticas, Universidad Nacional Autónoma de México (UNAM), Área de la Investigación Científica, Circuito exterior, Ciudad Universitaria, 04510, Mexico City, Mexico


We prove that given a germ of a generalized real analytic function in three variables, there exists a finite sequence of global blowing-up morphisms such that the total transform of the initial germ is locally of monomial type with respect to the generalized variables.

2020 Math. Subj. Class. 14E15, 14M25, 30D60, 32C05, 32S45.

Keywords: Combinatorial blowing-up morphism, combinatorial monomialization, generalized power series, linear representation of quivers, Newton polyhedron.

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