Given a smooth cubic hypersurface X over a finite field of characteristic greater than 3 and two generic points on X, we use a function field analogue of the Hardy–Littlewood circle method to obtain an asymptotic formula for the number of degree d k‐rational curves on X passing through those two points. We use this to deduce the dimension and irreducibility of the moduli space parametrising such curves, for large enough d.

中文翻译：

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有限域上立方超曲面的有理曲线

给定一个平滑三次超曲面X超过特性更大的有限域比3个两个通用点X，我们使用哈代-李特尔伍德圆法的函数的场类似物以获得渐近式为度数ð ķ -rational曲线在X上通过这两个点。对于足够大的d，我们用它来推导这些曲线的模空间参数化的尺寸和不可约性。