Analytic equivalence of normal crossing functions on a real analytic manifold

Details Analytic equivalence of normal crossing functions on a real analytic manifold Analytic equivalence of normal crossing functions on a real analytic manifold

2008-11-27

arxiv.org/abs/0811.4569v2

Mathematics

Algebraic Geometry

Scientific paper

By Hironaka Desingularization Theorem, any real analytic function has only normal crossing singularities after a suitable modification. We focus on the analytic equivalence of such functions with only normal crossing singularities. We prove that for such functions $C^{\infty}$ right equivalence implies analytic equivalence. We prove moreover that the cardinality of the set of equivalence classes is zero or countable.

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