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On the classification of Togliatti systems

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In [MeMR], Mezzetti and Mir\'{o}-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.

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
On the classification of Togliatti systems