منابع مشابه
An integral generalization of the Gusein-Zade–Natanzon theorem
One of the useful methods of the singularity theory, the method of real morsifications [AC0, GZ] (see also [AGV]) reduces the study of discrete topological invariants of a critical point of a holomorphic function in two variables to the study of some real plane curves immersed into a disk with only simple double points of self-intersection. For the closed real immersed plane curves V.I.Arnold [...
متن کاملPoincaré series and zeta function for an irreducible plane curve singularity
The Poincaré series of an irreducible plane curve singularity equals the ζ-function of its monodromy, by a result of Campillo, Delgado and GuseinZade. We derive this fact from a formula of Ebeling and Gusein-Zade relating the Poincaré series of a quasi-homogeneous complete intersection singularity to the Saito dual of a product of ζ-functions. Several cases are known where the ζ-function of the...
متن کاملOn the Motivic Measure on the Space of Functions
Motivic measure on the space of functions was introduced by Campillo, Delgado, and Gusein-Zade as an analog of the motivic measure on the space of arcs. In this paper we prove that the measure on the space of functions can be related to the motivic measure on the space of arcs by a factor, which can be defined explicitly in geometric terms. This provides a possibility to rewrite motivic integra...
متن کاملJa n 20 07 On the motivic measure on the space of functions
Motivic measure on the space of functions was introduced by Campillo, Delgado and Gusein-Zade as an analog of the motivic measure on the space of arcs . In this paper we prove that the measure on the space of functions can be related to the motivic measure on the space of arcs by a factor, which can be defined explicitly in geometric terms. This provides a possibility to rewrite motivic integra...
متن کاملM ay 2 00 2 Center conditions : Rigidity of logarithmic differential equations
In this paper we prove that any degree d deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again. This is a generalization of Ilyashenko’s result on Hamiltonian differential equations. The main tools are PicardLefschetz theory of a polynomial with complex coefficients in two variables, specially the Gusein-Zade/A’Campo’s theorem o...
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ژورنال
عنوان ژورنال: International Language, Literature and Folklore Researchers Journal
سال: 2018
ISSN: 2147-8872
DOI: 10.12992/turuk465