For tensors one beyond boundary format, codimension of singular vector span inside critical space equals dim of a cohomology kernel; an infinite family of order-3 tensors shows maximal rather than minimal codimension.
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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.
citing papers explorer
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On defective spans of singular vector tuples beyond the boundary format
For tensors one beyond boundary format, codimension of singular vector span inside critical space equals dim of a cohomology kernel; an infinite family of order-3 tensors shows maximal rather than minimal codimension.
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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.