On the identifiability of ternary forms

We describe a new method to determine the minimality and identifiability of a Waring decomposition A of a specific form (symmetric tensor) T in three variables. Our method, which is based on the Hilbert function of A, can distinguish between forms in the span of the Veronese image of A, which in general contains both identifiable and not identifiable points, depending on the choice of coefficients in the decomposition. This makes our method applicable for all values of the length r of the decomposition, from 2 up to the generic rank, a range which was not achievable before. Though the method in principle can handle all cases of specific ternary forms, we introduce and describe it in details for forms of degree 8.