On the description of identifiable quartics.

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 ≥ 9 , filling the gap between rank ≤ 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. [ABSTRACT FROM AUTHOR]