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arXiv · 2302.03715

Decompositions and Terracini loci of cubic forms of low rank

Luca Chiantini·Fulvio Gesmundo
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Abstract

We study Waring rank decompositions for cubic forms of rank $n+2$ in $n+1$ variables. In this setting, we prove that if a concise form has more than one non-redundant decomposition of length $n+2$, then all such decompositions share at least $n-3$ elements, and the remaining elements lie in a special configuration. Following this result, we give a detailed description of the $(n+2)$-th Terracini locus of the third Veronese embedding of $n$-dimensional projective space.

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Luca Chiantini, Fulvio Gesmundo. 2023-02-07. Decompositions and Terracini loci of cubic forms of low rank. https://doi.org/10.1090/conm%2F805%2F16131

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