Katsunori Iwasaki
Published 2008-09-09, updated 2008-10-31Version 3
We announce some results which might bring a new insight into the classification of algebraic solutions to the sixth Painleve equation. The main results consist of the rationality of parameters, trigonometric Diophantine conditions, and what the author calls the Tetrahedral Theorem regarding the absence of algebraic solutions in certain situations. The method is based on fruitful interactions between the moduli theoretical formulation of Painleve VI and dynamics on character varieties via the Riemann-Hilbert correspondence.
Comments: 16 pages, 9 figures, 1 table. A contribution to the Proceedings of the Conference on Exact WKB Analysis and Microlocal Analysis in RIMS, Kyoto, May, 2008
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