On the typical rank of real binary forms

Details On the typical rank of real binary forms On the typical rank of real binary forms

2009-09-26

arxiv.org/abs/0909.4865v1

Mathematics

Algebraic Geometry

12 pages, 2 figures

Scientific paper

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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