Moduli spaces of a family of topologically non quasi-homogeneous functions

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2018-10-31 DOI:10.5565/PUBLMAT6311902

J. Loubani

引用次数: 1

Abstract

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 and the quasi homogeneous case 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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拓扑非拟齐次函数族的模空间

我们考虑一个复解析函数胚在两个变量中的拓扑类，它不属于它的雅可比理想。这样的函数不是拟齐次的。这一类中的每个元素f都会引发一个叶理芽（df=0）。类似于Genzmer和Paul处理的齐次情形和拟齐次情形，我们描述了这类叶理的局部模量空间，并给出了解析正规形式。我们还证明了这些正规形式的唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.