2016/11/30 by Emilia Mezzetti, Rosa M. Miró‐Roig, Rosa Maria Miró-Roig
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Combinatorics #Commutative Algebra and Its Applications #Diagonal #Discrete mathematics #Homogeneous #Invariant (physics) #Mathematical analysis #Mathematics #Monomial #Polynomial #Polynomial and algebraic computation #Polynomial ring #Prime (order theory) #Prime power #Pure mathematics #math.AC #math.AG #msc:13E10 #msc:14M25 #msc:14N05 #msc:14N15 #msc:53A20
paper · pdf · doi:10.1016/j.jalgebra.2018.05.014
published as J. Algebra 509 (2018), 263-291 · 28 pages, 1 figure; final version published in Journal of Algebra
openalex publication_date 2018/05/19 · arxiv created 2018/09/06 · arxiv updated 2018/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the homogeneous artinian ideals of the polynomial ring K[x,y,z], generated by the homogenous polynomials of degree d which are invariant under an action of the cyclic group \mathbb Z/d\mathbb Z, 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.