On the maximum rank of a real binary form
Algebraic Geometry
2010-06-29 v1 Numerical Analysis
Abstract
We show that a real homogeneous polynomial f(x,y) with distinct roots and degree d greater or equal than 3 has d real roots if and only if for any (a,b) not equal to (0,0) the polynomial af_x+bf_y has d-1 real roots. This answers to a question posed by P. Comon and G. Ottaviani, and shows that the interior part of the locus of degree d binary real binary forms of rank equal to d is given exactly by the forms with d real roots.
Keywords
Cite
@article{arxiv.1006.5127,
title = {On the maximum rank of a real binary form},
author = {Antonio Causa and Riccardo Re},
journal= {arXiv preprint arXiv:1006.5127},
year = {2010}
}
Comments
To appear in Annali di Matematica Pura ed Applicata