12,342 research outputs found
Toric embedded resolutions of quasi-ordinary hypersurface singularities
We build two embedded resolution procedures of a quasi-ordinary singularity
of complex analytic hypersurface, by using toric morphisms which depend only on
the characteristic monomials associated to a quasi-ordinary projection of the
singularity. This result answers an open problem of Lipman in Equisingularity
and simultaneous resolution of singularities, Resolution of Singularities,
Progress in Mathematics No. 181, 2000, 485-503. In the first procedure the
singularity is embedded as hypersurface. In the second procedure, which is
inspired by a work of Goldin and Teissier for plane curves (see Resolving
singularities of plane analytic branches with one toric morphism,loc. cit.,
pages 315-340), we re-embed the singularity in an affine space of bigger
dimension in such a way that one toric morphism provides its embedded
resolution. We compare both procedures and we show that they coincide under
suitable hypothesis.Comment: To apear in Annales de l'Institut Fourier (Grenoble
Bijectiveness of the Nash Map for Quasi-Ordinary Hypersurface Singularities
In this paper we give a positive answer to a question of Nash concerning the
arc space of a singularity, for the class of quasi-ordinary hypersurface
singularities, extending to this case previous results and techniques of
Shihoko Ishii.Comment: comments and references adde
Optimal pre-merger notification mechanisms - incentives and efficiency of mandatory and voluntary schemes
The authors compare the two merger control systems currently employed worldwide: a mandatory system based on merger size threshold and a voluntary system with ex-post monitoring and fines. The voluntary system possesses two informational advantages: (i) the enforcement agency employs more information -verifiable and non verifiable parameters- to decide the set of mergers to investigate, and (ii) the first move of merging firms reveals useful information to the agency about the competitive risk of a merger. If fines for undue omission to notify are upward limited, then a mixed mechanism is optimal, where small transactions are under a voluntary regime while the big mergers are obliged to report. Remedies for fixing anticompetitive mergers act as an instrument that induces firms to notify the operation, improving further the advantage of the voluntary mechanism.Microfinance,Bankruptcy and Resolution of Financial Distress,Corporate Law,Economic Theory&Research,Small Scale Enterprise
Toric Geometry and the Semple-Nash modification
This paper proposes some material towards a theory of general toric varieties
without the assumption of normality. Their combinatorial description involves a
fan to which is attached a set of semigroups subjected to gluing-up conditions.
In particular it contains a combinatorial construction of the blowing up of a
sheaf of monomial ideals on a toric variety. In the second part it is shown
that over an algebraically closed base field of zero characteristic the
Semple-Nash modification of a general toric variety is isomorphic to the
blowing up of the sheaf of logarithmic jacobian ideals and that in any
characteristic this blowing-up is an isomorphism if and only if the toric
variety is non singular. In the second part we prove that orders on the lattice
of monomials (toric valuations) of maximal rank are uniformized by iterated
Sempla-Nash modifications.Comment: New version. Appeared in "Revista de la Real Academia de Ciencias
Exactas, Fisicas y Naturales, Serie A Matematicas", October 2012 (Electronic
Multi-Harnack smoothings of real plane branches
We introduce a new method for the construction of smoothings of a real plane
branch by using Viro Patchworking method. Since real plane branches
are Newton degenerated in general, we cannot apply Viro Patchworking method
directly. Instead we apply the Patchworking method for certain Newton non
degenerate curve singularities with several branches. These singularities
appear as a result of iterating deformations of the strict transforms of the
branch at certain infinitely near points of the toric embedded resolution of
singularities of . We characterize the -smoothings obtained by this
method by the local data. In particular, we analyze the class of multi-Harnack
smoothings, those smoothings arising in a sequence -smoothings of the strict
transforms of (C,0) which are in maximal position with respect to the
coordinate lines. We prove that there is a unique the topological type of
multi-Harnack smoothings, which is determined by the complex equisingularity
type of the branch. This result is a local version of a recent Theorem of
Mikhalkin
Motivic Milnor fiber of a quasi-ordinary hypersurface
Let be a germ of complex analytic function at
such that its zero level defines an irreducible germ of quasi-ordinary
hypersurface . We describe the motivic Igusa zeta function, the motivic
Milnor fibre and the Hodge-Steenbrink spectrum of at 0 in terms of
topological invariants of the quasi-ordinary hypersurface
Decomposition in bunches of the critical locus of a quasi-ordinary map
A polar hypersurface P of a complex analytic hypersurface germ, f=0, can be
investigated by analyzing the invariance of certain Newton polyhedra associated
to the image of P, with respect to suitable coordinates, by certain morphisms
appropriately associated to f. We develop this general principle of Teissier
(see Varietes polaires. I. Invariants polaires des singularites
d'hypersurfaces, Invent. Math. 40 (1977), 3, 267-292) when f=0 is a
quasi-ordinary hypersurface germ and P is the polar hypersurface associated to
any quasi-ordinary projection of f=0. We build a decomposition of P in bunches
of branches which characterizes the embedded topological type of the
irreducible components of f=0. This decomposition is characterized also by some
properties of the strict transform of P by the toric embedded resolution of f=0
given by the second author in a paper which will appear in Annal. Inst. Fourier
(Grenoble). In the plane curve case this result provides a simple algebraic
proof of the main theorem of Le, Michel and Weber in "Sur le comportement des
polaires associees aux germes de courbes planes", Compositio Math, 72, (1989),
1, 87-113
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