We show that a real binary form f of degree n has n distinct real roots if and only if for any (α, β) ε ℝ2\{0} all the forms αfx + βfy have n - 1 distinct real roots. This answers to a question of Comon and Ottaviani (On the typical rank of real binary forms, available at arXiv:math/0909. 4865, 2009), and allows to complete their argument to show that f has symmetric rank n if and only if it has n distinct real roots.
On the maximum rank of a real binary form
CAUSA, Antonio;RE, Riccardo
2010-01-01
Abstract
We show that a real binary form f of degree n has n distinct real roots if and only if for any (α, β) ε ℝ2\{0} all the forms αfx + βfy have n - 1 distinct real roots. This answers to a question of Comon and Ottaviani (On the typical rank of real binary forms, available at arXiv:math/0909. 4865, 2009), and allows to complete their argument to show that f has symmetric rank n if and only if it has n distinct real roots.File in questo prodotto:
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