Brieskorn Module and Center Conditions: Pull-Back of Differential Equations in Projective Space

Creative Commons License

Zare Y., TANABE S.

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, vol.27, no.4, pp.799-816, 2021 (SCI-Expanded) identifier identifier

  • 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
  • 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.