On the typical rank of real binary forms

2009/09/26 by Comon, Pierre, Ottaviani, Giorgio
#13P05 #14N05 #15A21 #15A69 #15A72 #Algebraic Geometry (math.AG) #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.0909.4865

Abstract

We determine the rank of a general real binary form of degree d=4 and d=5. In the case d=5, the possible values of the rank of such general forms are 3,4,5. The existence of three typical ranks was unexpected. We prove that a real binary form of degree d with d real roots has rank d.

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