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.

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. Proceedings of the London Mathematical Society, 2012, 104 (6), pp.1121-1170. ⟨10.1112/plms/pdr064⟩. ⟨hal-00342561v2⟩