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Quasi-ordinary singularities and Newton trees

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Artal Bartolo, Enrique and Cassou-Noguès, Pierrette and Luengo Velasco, Ignacio and Melle Hernández, Alejandro (2013) Quasi-ordinary singularities and Newton trees. Moscow Mathematical Journal , 13 (3). pp. 365-398. ISSN 1609-3321

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Official URL: http://www.mathjournals.org/mmj/2013-013-003/2013-013-003-001.html


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http://arxiv.org/abs/1203.1704UNSPECIFIED


Abstract

In this paper we study some properties of the class of nu-quasi-ordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize quasi-ordinary hypersurface singularities among nu-quasi-ordinary hypersurface singularities in terms of their Newton tree. A formula to compute the discriminant of a quasi-ordinary 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 quasi-ordinary 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 quasi-ordinary singularity in general. It does if we know that the Newton tree of the quasi-ordinary singularity has only one arrow.


Item Type:Article
Uncontrolled Keywords:Quasi-ordinary 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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