Produção Nacional
Revisado por pares
Gaps in the number of generators of monomial Togliatti systems
2018; Elsevier BV; Volume: 223; Issue: 4 Linguagem: Inglês
10.1016/j.jpaa.2018.07.009
ISSN1873-1376
AutoresCharles Almeida, Aline V. Andrade, Rosa M. Miró-Roig,
Tópico(s)Advanced Combinatorial Mathematics
ResumoLet Id,n⊂k[x0,⋯,xn] be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators μ(Id,n) of Id,n lies in the interval [2n+1,(n+d−1n−1)]. In this paper, we prove that for n≥4 and d≥3, the integer values in [2n+3,3n−1] cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems Id,n⊂k[x0,⋯,xn] of forms of degree d with μ(Id,n)=2n+2 or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for n=4, d≥3 and μ∈[9,(d+33)]∖{11} there exists a minimal monomial Togliatti system Id,n⊂k[x0,⋯,xn] of forms of degree d with μ(In,d)=μ.
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