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Quasi-ordinary singularities and Newton trees

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Artal Bartolo, Enrique y Cassou-Noguès, Pierrette y Luengo Velasco, Ignacio y 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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URL Oficial: http://www.mathjournals.org/mmj/2013-013-003/2013-013-003-001.html


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http://arxiv.org/abs/1203.1704SIN ESPECIFICAR


Resumen

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.


Tipo de documento:Artículo
Palabras clave:Quasi-ordinary singularities; resultant; factorization
Materias:Ciencias > Matemáticas > Álgebra
Código ID:23232
Depositado:17 Oct 2013 12:00
Última Modificación:07 Feb 2014 10:58

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