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arXiv · 1302.4338

Geometric Triviality of the Strongly Minimal Second Painlev\'e equations

Joel Nagloo
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Abstract

We show that the strongly minimal second Painlev\'e equation (y" = 2y^3+ty+\alpha) is geometrically trivial, that is we show that if y_1,...,y_n are distinct solutions such that y_1,y_1',y_2,y_2',...,y_n,y_n' are algebraically dependent over C(t), then already for some i<j, y_i,y_i',y_j,y_j' are algebraically dependent over C(t). This gives an extension of some recent result for the second Painlev\'e equation to the non generic parameters.

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Joel Nagloo. 2013-02-18. Geometric Triviality of the Strongly Minimal Second Painlev\'e equations. https://doi.org/10.1016/j.apal.2014.11.008

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