Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of them. We show that, under suitable assumptions on the degree of the curves and the dimensions of the two given ambient projective spaces, the number of curves and projections fulfilling the requirements is finite. Using standard techniques in intersection theory and the Bott residue formula, we compute this number.

中文翻译：

---

计算有理曲线的投影

给定两个射影空间中的两条同阶的一般有理曲线，可以问是否存在第三条同阶的第三条有理曲线同时投影到这两个空间。我们表明，在对曲线的度数和两个给定的环境投影空间的维度进行适当假设的情况下，满足要求的曲线和投影的数量是有限的。使用相交理论中的标准技术和 Bott 残差公式，我们计算了这个数字。