On the description of identifiable quartics

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 $\ge 9$, filling the gap between rank $\le 8$, 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.

KEYWORDS:

• Symmetric tensors
• identifiability
• Hilbert function
• Liason procedure
• Serre's construction

AMS CLASSIFICATIONS:

• 14N07
• 14J70
• 14C20
• 14N05
• 15A69
• 15A72

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are members of the Italian GNSAGA-INDAM.