For binary forms, forms admitting an eigenvector in a minimal Waring decomposition form a codimension-one subvariety of the secant variety, and any eigenvector increases rank for subgeneric ranks and for generic odd-degree forms.
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On Waring rank jumps via critical rank-one approximations
For binary forms, forms admitting an eigenvector in a minimal Waring decomposition form a codimension-one subvariety of the secant variety, and any eigenvector increases rank for subgeneric ranks and for generic odd-degree forms.