Local Monomialization of Analytic Maps

TL;DR

This paper proves local monomialization theorems for analytic maps between complex and real analytic spaces, extending previous algebraic results to the analytic setting, thus broadening the understanding of morphism simplification.

Contribution

It generalizes the local monomialization theorem from algebraic varieties to complex and real analytic spaces, providing new tools for analyzing analytic morphisms.

Findings

Proved local monomialization theorems for analytic morphisms

Extended algebraic monomialization results to analytic spaces

Enhanced understanding of morphism structure in analytic geometry

Abstract

In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of characteristic zero proven in the author's earlier papers "Local monomialization of morphisms", Asterisque 260 (1999) and "Local monomialization of transcendental extensions", Annales de l'institut Fourier, 1517 - 1586.