We prove that the Hilbert schemes of 2-points on rational surfaces are numerically rationally connected. The main idea is to show that certain 3-point genus-0 Gromov–Witten invariant of the Hilbert scheme of two points on the complex projective plane is positive and can be calculated enumeratively.

中文翻译：

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关于有理面上两点的 Hilbert 格式的数值有理连通性

我们证明了有理面上两点的希尔伯特方案在数值上是有理连接的。主要思想是证明复射影平面上两点的希尔伯特方案的某个 3 点属 0 Gromov-Witten 不变量是正的，并且可以枚举计算。