RT Journal Article
T1 Quasi-ordinary singularities and Newton trees
A1 Artal Bartolo, Enrique
A1 Cassou-Noguès, Pierrette
A1 Luengo Velasco, Ignacio
A1 Melle Hernández, Alejandro
AB 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.
PB Independent University of Moscow
SN 1609-3321
YR 2013
FD 2013
LK https://hdl.handle.net/20.500.14352/33369
UL https://hdl.handle.net/20.500.14352/33369
LA eng
DS Docta Complutense
RD 13 may 2025