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

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Zare Y., TANABE S.

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, cilt.27, sa.4, ss.799-816, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s10883-021-09556-z
  • Dergi Adı: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • Derginin Tarandığı İndeksler: 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
  • Sayfa Sayıları: ss.799-816
  • Anahtar Kelimeler: Holomorphic foliations, Picard-Lefschetz theory
  • Galatasaray Üniversitesi Adresli: Evet

Özet

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.