Resolution of singularities in Denjoy-Carleman classes

• Edward Bierstone ^[1] ; Pierre D. Milman ^[1]
  1. [1] University of Toronto

     University of Toronto

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 10, Nº. 1, 2004, págs. 1-28
• Idioma: inglés
• DOI: 10.1007/s00029-004-0327-0
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• Resumen

  • We show that a version of the desingularization theorem of Hironaka C∞ holds for certain classes of functions (essentially, for subrings that exclude flat functions and are closed under differentiation and the solution of implicit equations). Examples are quasianalytic classes, introduced by E. Borel a century ago and characterized by the Denjoy-Carleman theorem. These classes have been poorly understood in dimension > 1. Resolution of singularities can be used to obtain many new results; for example, topological Noetherianity, curve selection, Łojasiewicz inequalities, division properties.