2017/10/07 by Rosa Maria Miró-Roig, Miró-Roig, Rosa Maria, Martí Salat +1
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.1710.03579
To appear in Communications in Algebra. arXiv admin note: text overlap with arXiv:1506.05914
arxiv created 2017/10/07 · arxiv updated 2017/10/11
In [MeMR], Mezzetti and Miró-Roig proved that the minimal number of generators μ(I) of a minimal (smooth) monomial Togliatti system I⊂ k[x0,\dotsc,xn] satisfies 2n+1≤ μ(I)≤ \binomn+d-1n-1 and they classify all smooth minimal monomial Togliatti systems I⊂ k[x0,\dotsc,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,\dotsc,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.