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Artal Bartolo, Enrique and CassouNoguès, Pierrette and Luengo Velasco, Ignacio and Melle Hernández, Alejandro (2013) Quasiordinary singularities and Newton trees. Moscow Mathematical Journal , 13 (3). pp. 365398. ISSN 16093321

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Official URL: http://www.mathjournals.org/mmj/2013013003/2013013003001.html
URL  URL Type 

http://arxiv.org/abs/1203.1704  UNSPECIFIED 
Abstract
In this paper we study some properties of the class of nuquasiordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize quasiordinary hypersurface singularities among nuquasiordinary hypersurface singularities in terms of their Newton tree. A formula to compute the discriminant of a quasiordinary Weierstrass polynomial in terms of the decorations of its Newton tree is given. This allows to compute the discriminant avoiding the use of determinants and even for non Weierstrass prepared polynomials. This is important for applications like algorithmic resolutions. We compare the Newton tree of a quasiordinary singularity and those of its curve transversal sections. We show that the Newton trees of the transversal sections do not give the tree of the quasiordinary singularity in general. It does if we know that the Newton tree of the quasiordinary singularity has only one arrow.
Item Type:  Article 

Uncontrolled Keywords:  Quasiordinary singularities; resultant; factorization 
Subjects:  Sciences > Mathematics > Algebra 
ID Code:  23232 
Deposited On:  17 Oct 2013 12:00 
Last Modified:  07 Feb 2014 10:58 
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