Stratified Reduction of Singularities of Generalized Analytic Functions

TL;DR

This paper extends the local reduction of singularities for generalized analytic functions to a global setting, demonstrating that such functions can be simplified to monomial form through a finite sequence of blow-ups.

Contribution

It provides the first global approach to reducing singularities of generalized analytic functions, building on previous local results by employing a finite sequence of blow-ups.

Findings

Functions can be transformed into monomial form near boundary divisors

Finite sequence of blow-ups suffices for global reduction

Achieves normal crossings divisor structure

Abstract

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde, Rolin and Sanz-S\'anchez it is established a result of local reduction of singularities for such a functions. In this paper we deal with a first approach of the global problem. Namely, we prove that a germ of generalized analytic function can be transformed by a finite sequence of blowing-ups with closed centers into a function which is locally of monomial type with respect to the coordinates defining the boundary of the manifold (a normal crossings divisor).