Segre Surfaces and Geometry of the Painlevé Equations
Abstract
Abstract In this paper, we consider a six parameter family of affine Segre surfaces embedded in $$\mathbb C^6$$ C 6 . For generic values of the parameters, this family is associated to the q -difference sixth Painlevé equation. We show that different limiting forms of this family give Segre surfaces that are isomorphic as affine varieties to the monodromy manifolds of each Painlevé differential equation.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Nonlinear Waves and Solitons
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Communications in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 407
- Issue
- 9
- Publication date
- 1 August 2026
- Language
- EN