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Flat structure and potential vector fields related with algebraic solutions to Painleve VI equation

Kato M., Mano T., Sekiguchi J.

Opuscula Mathematica

2018

Vol. 38, no. 2

201--252

A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painleve VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.