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}
}