On the description of identifiable quartics

Elena Angelini; Luca Chiantini

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arXiv · 2106.06730

On the description of identifiable quartics

Elena Angelini·Luca Chiantini

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Abstract

In this paper we study the identifiability of specific forms (symmetric tensors), with the target of extending recent methods for the case of $3$ variables to more general cases. In particular, we focus on forms of degree $4$ in $5$ variables. By means of tools coming from classical algebraic geometry, such as Hilbert function, liaison procedure and Serre's construction, we give a complete geometric description and criteria of identifiability for ranks $\geq 9$, filling the gap between rank $\leq 8$, covered by Kruskal's criterion, and $15$, the rank of a general quartic in $5$ variables. For the case $r=12$, we construct an effective algorithm that guarantees that a given decomposition is unique.

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Elena Angelini, Luca Chiantini. 2021-06-12. On the description of identifiable quartics. https://arxiv.org/abs/2106.06730

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