Sixth Painlev\'e Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
An algebro-geometric setting for the study of the Painlev\'e VI equation is introduced. Hamiltonian form of the equation is realized on a twisted relative cotangent bundle to the universal elliptic curve with labelled points of order two. Relations with the theory of elliptic functions and the quantum cohomology of projective plane are discussed.
Keywords
Cite
@article{arxiv.alg-geom/9605010,
title = {Sixth Painlev\'e Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$},
author = {Yu. I. Manin},
journal= {arXiv preprint arXiv:alg-geom/9605010},
year = {2008}
}
Comments
AMS-Tex file, 22 pages, no figures