English

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.

Keywords

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

R2 v1 2026-06-24T11:13:42.727Z