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Togliatti systems and Galois coverings

2018; Elsevier BV; Volume: 509; Linguagem: Inglês

10.1016/j.jalgebra.2018.05.014

1090-266X

Emilia Mezzetti, Rosa M. Miró-Roig,

Polynomial and algebraic computation

We study the homogeneous artinian ideals of the polynomial ring K[x,y,z] generated by the homogeneous polynomials of degree d which are invariant under an action of the cyclic group Z/dZ, for any d≥3. We prove that they are all monomial Togliatti systems, and that they are minimal if the action is defined by a diagonal matrix having on the diagonal (1,e,ea), where e is a primitive d-th root of the unity. We get a complete description when d is prime or a power of a prime. We also establish the relation of these systems with linear Ceva configurations.