强极小第二类Painlevé方程的几何平凡性
Geometric Triviality of the Strongly Minimal Second Painlevé equations
摘要：
本文证明了强极小第二类Painlevé方程（y”= 2y^3+ty+α）是几何平凡的，即如果y_1，.，y_n是不同的解，使得y_1，y_1'，y_2，y_2'，.，y_n，y_n'在C（t）上代数依赖，则对某些i<j，y_i，y_i'，y_j，y_j'在C（t）上代数依赖.这给出了推广的一些最近的结果为第二Painlevé方程的非通用参数。
英文摘要：
We show that the strongly minimal second Painlevé equation (y" = 2y^3+ty+α) 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.
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