Segre surfaces and geometry of the Painlev\'e equations
Mathematical Physics
2026-03-23 v2 Algebraic Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
In this paper, we consider a six parameter family of affine Segre surfaces embedded in . For generic values of the parameters, this family is associated to the -difference sixth Painlev\'e equation. We show that different limiting forms of this family give Segre surfaces that are isomorphic as affine varieties to the the monodromy manifolds of each Painlev\'e differential equation.
Keywords
Cite
@article{arxiv.2405.10541,
title = {Segre surfaces and geometry of the Painlev\'e equations},
author = {Nalini Joshi and Marta Mazzocco and Pieter Roffelsen},
journal= {arXiv preprint arXiv:2405.10541},
year = {2026}
}
Comments
Fixed typos, added references and two remarks, Remark 4.1 and Remark 6.4