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EnglishWe 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 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.
| Titolo: | Togliatti systems and Galois coverings |
| Autori: | |
| Data di pubblicazione: | 2018 |
| Data ahead of print: | 19-mag-2018 |
| Stato di pubblicazione: | Pubblicato |
| Rivista: | |
| Abstract: | 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 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. |
| Handle: | http://hdl.handle.net/11368/2929099 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jalgebra.2018.05.014 |
| URL: | https://doi.org/10.1016/j.jalgebra.2018.05.014 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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http://hdl.handle.net/11368/2929099
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