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


Zare Y., TANABE S.

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2021
  • Doi Number: 10.1007/s10883-021-09556-z
  • Title of Journal : JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS

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.