Geometric Triviality of the Strongly Minimal Second Painlev\'e equations
Algebraic Geometry
2017-08-16 v1
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.
Keywords
Cite
@article{arxiv.1302.4338,
title = {Geometric Triviality of the Strongly Minimal Second Painlev\'e equations},
author = {Joel Nagloo},
journal= {arXiv preprint arXiv:1302.4338},
year = {2017}
}