Laplace equations, Lefschetz properties and line arrangements

In this note we generalize the main result in the previous work on JLMS on artinian ideals failing Lefschetz properties, varieties satisfying Laplace equations and existence of suitable singular hypersurfaces. Moreover we characterize the minimally generation of ideals generated by power of linear forms by the conguration of their dual points in the projective plane. Finally we show the equivalence among failing SLP, Laplace equations and unexpected curves