Monomialization of a quasianalytic morphism
| Autor: | da Silva, André Belotto, Bierstone, Edward |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove a monomialization theorem for mappings in general classes of infinitely differentiable functions that are called quasianalytic. Examples include Denjoy-Carleman classes, the class of $\cC^\infty$ functions definable in a polynomially bounded $o$-minimal structure, as well as the classes of real- or complex analytic functions, and algebraic functions over any field of characteristic zero. The monomialization theorem asserts that a mapping in a quasianalytic class can be transformed to a mapping whose components are monomials with respect to suitable local coordinates, by sequences of simple modifications of the source and target -- local blowings-up and power substitutions in the real cases, in general, and local blowings-up alone in the algebraic or analytic cases. Monomialization is a version of resolution of singularities for a mapping. We show that it is not possible, in general, to monomialize by global blowings-up, even in the real-analytic case. Comment: 66 pages; revised version, theorems unchanged; to appear in Ann. Sci. Ecole Norm. Sup |
| Databáze: | arXiv |
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