English

Brieskorn module and Center conditions: pull-back of differential equations in projective space

Dynamical Systems 2020-10-05 v2 Complex Variables

Abstract

The moduli space of algebraic foliations on P2 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 set of pull-back foliations forms an irreducible component of the moduli space. The main tools are the Picard-Lefschetz theory of a rational function in two variables, period integrals, and the Brieskorn module.

Keywords

Cite

@article{arxiv.2009.06771,
  title  = {Brieskorn module and Center conditions: pull-back of differential equations in projective space},
  author = {Yadollah Zare and Susumu Tanabe},
  journal= {arXiv preprint arXiv:2009.06771},
  year   = {2020}
}