Resolution of singularities in DenjoyCarleman classes
Abstract
We show that a version of the desingularization theorem of Hironaka holds for certain classes of infinitely differentiable 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 DenjoyCarleman 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, Lojasiewicz inequalities, division properties.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2001
 arXiv:
 arXiv:math/0108204
 Bibcode:
 2001math......8204B
 Keywords:

 Complex Variables;
 Algebraic Geometry;
 26E10;
 32S45;
 58C25
 EPrint:
 35 pages, AMSTEX