Rectilinearization of sub analytic sets as a consequence of local monomialization

TL;DR

This paper presents a new proof of Hironaka's rectilinearization theorem by deriving it from a local monomialization theorem applicable to complex and real analytic morphisms.

Contribution

It introduces a novel approach linking local monomialization to rectilinearization, providing a new proof of Hironaka's theorem.

Findings

New proof of rectilinearization theorem

Connection between monomialization and rectilinearization

Applicable to complex and real analytic morphisms

Abstract

We give a new proof of the rectilinearization theorem of Hironaka. We deduce rectilinearization as a consequence of our theorem on local monomialization for complex and real analytic morphisms.