Resolution of singularities in Denjoy-Carleman classes

Details Resolution of singularities in Denjoy-Carleman classes Resolution of singularities in Denjoy-Carleman classes

2001-08-29

arxiv.org/abs/math/0108204v1

Mathematics

Complex Variables

35 pages, AMSTEX

Scientific paper

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 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, Lojasiewicz inequalities, division properties.

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