Analytic equivalence of normal crossing functions on a real analytic manifold

Goulwen Fichou (1) , Masahiro Shiota (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Graduate School of Mathematics [Nagoya]

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. We apply these results to study the cardinality of the set of equivalence classes for almost blow-analytic equivalence.

Mots clés: Real analytic functions; desingularization; normal crossing

Domaines: Géométrie algébrique [math.AG]

Goulwen Fichou, Masahiro Shiota. Analytic equivalence of normal crossing functions on a real analytic manifold. 2008. ⟨hal-00342561v1⟩