Irreducibility criterion for quasi-ordinary polynomials

Journal of Singularities
volume 4 (2012), 23-34

Received: 14 October 2010. Received in revised form: 19 December 2011.

DOI: 10.5427/jsing.2012.4b

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Abstract:

Using the notion of approximate roots and that of generalized Newton sets, we give a local criterion for a quasi ordinary polynomial to be irreducible. Such a criterion is useful in the study of singularities of quasi-ordinary hypersurfaces. It generalizes the criterion given by S.S. Abhyankar for algebraic plane curves.

Mathematical Subject Classification:

32S25, 32S7

Author(s) information:

Abdallah Assi
Université d'Angers, Mathématiques
49045 Angers cedex 01
France
email: assi@univ-angers.fr