Waring rank of binary forms, harmonic cross-ratio and golden ratio
Algebraic Geometry
2020-02-25 v3
Abstract
We discuss the Waring rank of binary forms of degree 4 and 5, without multiple factors, and point out unexpected relations to the harmonic cross-ratio, j-invariants and the golden ratio. These computations of ranks for binary forms are used to show that the combinatorics of a line arrangement in the complex projective plane does not determine the Waring rank of the defining equation even in very simple situations.
Keywords
Cite
@article{arxiv.2002.05617,
title = {Waring rank of binary forms, harmonic cross-ratio and golden ratio},
author = {Alexandru Dimca and Gabriel Sticlaru},
journal= {arXiv preprint arXiv:2002.05617},
year = {2020}
}
Comments
v.3: We relate our results to results in the paper L. Brustenga i Moncus\' i, S. K. Masuti, On the Waring rank of binary forms: the binomial formula and a dihedral cover of rank two forms, arXiv:1901.08320