1. A counterexample to a conjecture on simultaneous Waring identifiability
- Author
-
Angelini, Elena
- Subjects
14N07, 15A69, 14N05, 13P05, 65H10, 15A72, 14Q20 ,Mathematics - Algebraic Geometry ,Computational Mathematics ,Algebra and Number Theory ,FOS: Mathematics ,Algebraic Geometry (math.AG) - Abstract
The new identifiable case appeared in \cite{AGMO}, together with the analysis on simultaneous identifiability of pairs of ternary forms recently developed in \cite{BG}, suggested the following conjecture towards a complete classification of all simultaneous Waring identifiable cases: for any $ d \geq 2 $, the general polynomial vectors consisting of $ d-1 $ ternary forms of degree $ d $ and a ternary form of degree $ d+1 $, with rank $ \frac{d^2+d+2}{2} $, are identifiable over $ \mathbf{C} $. In this paper, by means of a computer-aided procedure inspired to the one described in \cite{AGMO}, we obtain that the case $ d = 4 $ contradicts the previous conjecture, admitting at least $ 36 $ complex simultaneous Waring decompositions (of length $ 11 $) instead of $ 1 $., Comment: 10 pages, accepted for publication on Journal of Symbolic Computation
- Published
- 2024