论文标题
特征点的配置
Configurations of eigenpoints
论文作者
论文摘要
该注释是由http://cubics.wikidot.com的问题16的动机：哪些在三个立方体表面的特征点中出现了三个空间中15分的配置？我们证明，射影n空间中的一般特征cheme是在平滑的确定表面上的两条合适的平滑确定曲线的完全相交。此外，我们证明，如果n = 3，则相反的结果在任何程度上为引用的问题提供答案。最后，我们表明，射影3空间中的任何一般点都可以放大到部分对称张量的特征cheme。
This note is motivated by the Question 16 of http://cubics.wikidot.com: Which configurations of 15 points in the projective 3-space arise as eigenpoints of a cubic surface? We prove that a general eigenscheme in the projective n-space is the complete intersection of two suitable smooth determinantal curves on a smooth determinantal surface. Moreover, we prove that the converse result holds if n=3, providing an answer in any degree to the cited question. Finally, we show that any general set of points in the projective 3-space can be enlarged to an eigenscheme of a partially symmetric tensor.
