Miró-Roig, Rosa M. (Rosa Maria)Colarte Gómez, Liena2019-02-272019-02-272018-06-28https://hdl.handle.net/2445/128969Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Rosa Maria Miró-Roig[en] Fixed $4 \leq d$ and a primitive $d$th root of unity $e$ we consider the ideal $I_{d}$ generated by all the $\mu$ monomials of degree $d$ invariant under the action of the diagonal matrix $M= Diag(1,e, e^{2},e^{3})$. We prove that $I_{d}$ is a monomial Galois Togliatti system ($GT$-system). We study the variety $F_{d}$ image of the Galois covering $\varphi_{Id}$ : $\mathbb{P}^{3}\rightarrow mathbb{P}^{\mu-1}$ with cyclic Galois group $\mathbb{Z}/d$ associated to $I_{d}$. We call this 3-dimensional variety $GT$-threefold. Finally, we demonstrate that the homogeneous ideal of $GT$-threefolds is a lattice ideal associated to a saturated partial character from $\mathbb{Z^\mu}$.40 p.application/pdfengcc-by-sa (c) Liena Colarte Gómez, 2018http://creativecommons.org/licenses/by-sa/3.0/es/Varietats tòriquesVarietats algebraiquesTreballs de fi de màsterGeometria diferencialGeometria projectivaAnells artiniansMòduls (Àlgebra)Toric varietiesAlgebraic varietiesMaster's thesesDifferential geometryProjective geometryArtin ringsModules (Algebra)info:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess