On the maximum rank of a real binary form

Antonio Causa; Riccardo Re

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arXiv · 1006.5127

On the maximum rank of a real binary form

Antonio Causa·Riccardo Re

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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.

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Antonio Causa, Riccardo Re. 2010-06-26. On the maximum rank of a real binary form. https://arxiv.org/abs/1006.5127

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