Gaps in the number of generators of monomial Togliatti systems |
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Authors: | Charles Almeida Aline V. Andrade Rosa M. Miró-Roig |
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Affiliation: | 1. Instituto de Matemática, Estatística e Computação Científica – UNICAMP, Rua Sérgio Buarque de Holanda 651, Distr. Barão Geraldo, CEP 13083-859, Campinas (SP), Brazil;2. Department de matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain |
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Abstract: | Let be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators of lies in the interval . In this paper, we prove that for and , the integer values in cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems of forms of degree d with or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for , and there exists a minimal monomial Togliatti system of forms of degree d with . |
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Keywords: | 13E10 14M25 14N05 14N15 53A20 |
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