High-rank ternary forms of even degree
| Autor: | Alessandro De Paris |
|---|---|
| Přispěvatelé: | DE PARIS, Alessandro |
| Rok vydání: | 2017 |
| Předmět: |
Monomial
15A21 14N15 13P99 Degree (graph theory) General Mathematics 010102 general mathematics Zero (complex analysis) Waring rank 010103 numerical & computational mathematics Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Upper and lower bounds Ternary form Combinatorics Mathematics - Algebraic Geometry Symmetric tensor Tensor rank FOS: Mathematics Rank (graph theory) 0101 mathematics Algebraically closed field Ternary operation Algebraic Geometry (math.AG) Mathematics |
| DOI: | 10.48550/arxiv.1706.04604 |
| Popis: | We exhibit, for each positive even degree, a ternary form of rank strictly greater than the maximum rank of monomials. Together with an earlier result in the odd case, this gives a lower bound of $$\begin{aligned} \left\lfloor \frac{d^2+2d+5}{4}\right\rfloor \;, \end{aligned}$$ for $$d\ge 2$$ , on the maximum rank of degree d ternary forms with coefficients in an algebraically closed field of characteristic zero. |
| Databáze: | OpenAIRE |
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