Submission date: 19 February 2013

Abstract:

We show that the strongly minimal second Painlevé 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 Painlevé equation to the non generic parameters.

Mathematics Subject Classification: 14H05, 34M55, 03C60, 14H70

Keywords and phrases:

Full text arXiv 1302.4338: pdf, ps.