Arc Criterion of Normal Embedding

  • Lev Birbrair
  • Rodrigo MendesEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)


We present a criterion of local normal embedding of a semialgebraic (or definable in a polynomially bounded o-minimal structure) germ contained in \(\mathbb R^n\) in terms of orders of contact of arcs. Namely, we prove that a semialgebraic germ is normally embedded if and only if for any pair of arcs, coming to this point the inner order of contact is equal to the outer order of contact.


Normal embedding Singularities 

1991 Mathematics Subject Classification

14B05 32S50 



We would like to thank Alexandre Fernandes, Edson Sampaio, Anne Pichon and Walter Neumann for useful discussions. We would like also to thank the anonymous referee for his patience and extremely useful comments and corrections.


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Authors and Affiliations

  1. 1.Departamento of MatemáticaUniversidade Federal do CearáFortalezaBrazil
  2. 2.Instituto de Ciências Exatas e da NaturezaUniversidade de Integração Internacional da Lusofonia Afro-Brasileira (unilab)AcarapeBrazil

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