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On the classification of Togliatti systems

2017; Taylor & Francis; Volume: 46; Issue: 6 Linguagem: Inglês

10.1080/00927872.2017.1388813

1532-4125

Rosa M. Miró-Roig, Martí Salat-Moltó,

Commutative Algebra and Its Applications

In [4 Mezzetti, E., Miró-Roig, R. M. (2016). The minimal number of generators of a Togliatti system. Annali di Matematica Pura ed Applicata 195:2077–2098. DOI: 10.1007/s10231-016-0554-y.[Crossref], [Web of Science ®] , [Google Scholar]], Mezzetti and Miró-Roig proved that the minimal number of generators μ(I) of a minimal (smooth) monomial Togliatti system I⊂k[x0,…,xn] satisfies 2n+1≤μ(I)≤(n+d−1n−1) and they classify all smooth minimal monomial Togliatti systems I⊂k[x0,…,xn] with 2n+1≤μ(I)≤2n+2. In this paper, we address the first open case. We classify all smooth monomial Togliatti systems I⊂k[x0,…,xn] of forms of degree d≥4 with μ(I) = 2n+3 and n≥2 and all monomial Togliatti systems I⊂k[x0,x1,x2] of forms of degree d≥6 with μ(I) = 7.