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arXiv · 2206.10656

Stratified Reduction of Singularities of Generalized Analytic Functions

B. Molina-Samper·J. Palma-Márquez·F. Sanz-Sánchez
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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).

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B. Molina-Samper, J. Palma-Márquez, F. Sanz-Sánchez. 2022-06-21. Stratified Reduction of Singularities of Generalized Analytic Functions. https://arxiv.org/abs/2206.10656

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