Let k be any field. Let be a degree hypersurface. Under some conditions, we prove that if for some extension with and , then for some extension with , , and . Moreover, if a K-solution is known explicitly, then we can compute explicitly as well. As an application, we improve upon a result by Coray on smooth cubic surfaces by showing that if for some extension with , then for some with .

中文翻译：

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超曲面上闭点的度数

令k为任意字段。让是一个学位超曲面。在某些条件下，我们证明如果为了一些扩展和和， 然后为了一些扩展和,， 和。此外，如果明确已知K解，那么我们可以计算也明确地表示。作为一个应用，我们改进了 Coray 在光滑立方表面上的结果通过证明如果为了一些扩展和， 然后对于一些和。