There is a mysterious connection between #algebraic #surfaces and solutions of non-linear differential equations called the #Painlevé equations. Marta Mazzocco
@unibirmingham Pieter Roffelsen and I
@sydney_uni show surprising variations on this connection: https://arxiv.org/abs/2405.10541
arXiv.orgSegre surfaces and geometry of the Painlevé equationsIn this paper, we consider a six parameter family of affine Segre surfaces embedded in $\mathbb C^6$. 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 the monodromy manifolds of each Painlevé differential equation.
