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 floor of (d^2+2d+5)/4,for d>=2, on the maximum rank of degree d ternary forms with coefficients in an algebraically closed field of characteristic zero.
High-rank ternary forms of even degree / DE PARIS, Alessandro. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 109:6(2017), pp. 505-510. [10.1007/s00013-017-1105-5]
High-rank ternary forms of even degree
DE PARIS, ALESSANDRO
2017
Abstract
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 floor of (d^2+2d+5)/4,for d>=2, on the maximum rank of degree d ternary forms with coefficients in an algebraically closed field of characteristic zero.File in questo prodotto:
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Open Access dal 02/10/2018
Descrizione: Accepted version. The final publication is available at Springer via http://dx.doi.org/10.1007/s00013-017-1105-5
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