Brieskorn Module and Center Conditions: Pull-Back of Differential Equations in Projective Space
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, vol.27, no.4, pp.799-816, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 27 Issue: 4
- Publication Date: 2021
- Doi Number: 10.1007/s10883-021-09556-z
- Journal Name: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.799-816
- Keywords: Holomorphic foliations, Picard-Lefschetz theory
- Open Archive Collection: AVESIS Open Access Collection
- Galatasaray University Affiliated: Yes
Abstract
The moduli space of algebraic foliations on P-2 of a fixed degree and with a center singularity has many irreducible components. We find a basis of the Brieskorn module defined for a rational function and prove that pull-back foliations forms an irreducible component of the moduli space. The main tools are Picard-Lefschetz theory of a rational function in two variables, period integrals and Brieskorn module.