JOURNAL OF ALGEBRA | 卷:509 |
Togliatti systems and Galois coverings | |
Article | |
Mezzetti, Emilia1  Miro-Roig, Rosa M.2  | |
[1] Univ Trieste, Dipartimento Matemat & Geosci, Sez Matemat & Informat, Via Valerio 12-1, I-34127 Trieste, Italy | |
[2] Fac Matemat & Informat, Dept Matemat & Informat, Gran Via Corts Catalanes 585, Barcelona 08007, Spain | |
关键词: Togliatti systems; Weak Lefschetz property; Galois coverings; Tonic varieties; | |
DOI : 10.1016/j.jalgebra.2018.05.014 | |
来源: Elsevier | |
【 摘 要 】
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, e(a)), 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. (C) 2018 Elsevier Inc. All rights reserved.
【 授权许可】
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