Open Access
2019 Moduli spaces of a family of topologically non quasi-homogeneous functions
Jinan Loubani
Publ. Mat. 63(1): 81-104 (2019). DOI: 10.5565/PUBLMAT6311902


We consider a topological class of a germ of complex analytic function in two variables which does not belong to its jacobian ideal. Such a function is not quasi homogeneous. Each element $f$ in this class induces a germ of foliation ($df = 0$). Proceeding similarly to the homogeneous case [2] and the quasi homogeneous case [3] treated by Genzmer and Paul, we describe the local moduli space of the foliations in this class and give analytic normal forms. We prove also the uniqueness of these normal forms.


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Jinan Loubani. "Moduli spaces of a family of topologically non quasi-homogeneous functions." Publ. Mat. 63 (1) 81 - 104, 2019.


Received: 28 February 2017; Revised: 27 September 2017; Published: 2019
First available in Project Euclid: 7 December 2018

zbMATH: 07040962
MathSciNet: MR3908787
Digital Object Identifier: 10.5565/PUBLMAT6311902

Primary: 32S65 , 34M35

Keywords: complex foliations , singularities

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 1 • 2019
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