Configurations of eigenpoints
Algebraic Geometry
2022-05-12 v1
Abstract
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.
Cite
@article{arxiv.2205.05196,
title = {Configurations of eigenpoints},
author = {Valentina Beorchia and Rosa M. Miró-Roig},
journal= {arXiv preprint arXiv:2205.05196},
year = {2022}
}
Comments
12 pages