Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$

Details Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$ Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$

1996-05-22

arxiv.org/abs/alg-geom/9605010v1

Mathematics

Algebraic Geometry

AMS-Tex file, 22 pages, no figures

Scientific paper

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.

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