On generic and maximal k-ranks of binary forms
Algebraic Geometry
2019-02-07 v1 Commutative Algebra
Abstract
In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic k-rank of complex-valued forms of any degree divisible by k in any number of variables. The second one (by the fourth author) deals with the maximal k-rank of binary forms. We settle the first conjecture in the cases of two variables and the second in the first non-trivial case of the 3-rd powers of quadratic binary forms.
Cite
@article{arxiv.1711.05014,
title = {On generic and maximal k-ranks of binary forms},
author = {Samuel Lundqvist and Alessandro Oneto and Bruce Reznick and Boris Shapiro},
journal= {arXiv preprint arXiv:1711.05014},
year = {2019}
}
Comments
17 pages, 1 figure