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arXiv · 2301.05276

Waring identifiability for powers of forms via degenerations

Alex Casarotti·Elisa Postinghel
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Abstract

We discuss an approach to the secant non-defectivity of the varieties parametrizing $k$-th powers of forms of degree $d$. It employs a Terracini type argument along with certain degeneration arguments, some of which are based on toric geometry. This implies a result on the identifiability of the Waring decompositions of general forms of degree kd as a sum of $k$-th powers of degree $d$ forms, for which an upper bound on the Waring rank was proposed by Fr\"oberg, Ottaviani and Shapiro.

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Alex Casarotti, Elisa Postinghel. 2023-01-12. Waring identifiability for powers of forms via degenerations. https://arxiv.org/abs/2301.05276

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