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Preprint Number 558
558. Joel Nagloo Geometric Triviality of the Strongly Minimal Second Painlevé
equations E-mail: 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: |

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