On the classification of Togliatti systems

Abstract

ABSTRACTIn [4], Mezzetti and Miró-Roig proved that the minimal number of generators μ(I) of a minimal (smooth) monomial Togliatti system satisfies and they classify all smooth minimal monomial Togliatti systems with 2n+1≤μ(I)≤2n+2. In this paper, we address the first open case. We classify all smooth monomial Togliatti systems of forms of degree d≥4 with μ(I) = 2n+3 and n≥2 and all monomial Togliatti systems of forms of degree d≥6 with μ(I) = 7.