تقرير
A counterexample to a conjecture on simultaneous Waring identifiability
| العنوان: | A counterexample to a conjecture on simultaneous Waring identifiability |
|---|---|
| المؤلفون: | Angelini, Elena |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 14N07, 15A69, 14N05, 13P05, 65H10, 15A72, 14Q20 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.03186 |
| رقم الأكسشن: | edsarx.2304.03186 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |