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http://hdl.handle.net/2445/128969
Title: | GT-Varieties |
Author: | Colarte Gómez, Liena |
Director/Tutor: | Miró-Roig, Rosa M. (Rosa Maria) |
Keywords: | Varietats tòriques Varietats algebraiques Treballs de fi de màster Geometria diferencial Geometria projectiva Anells artinians Mòduls (Àlgebra) Toric varieties Algebraic varieties Master's theses Differential geometry Projective geometry Artin rings Modules (Algebra) |
Issue Date: | 28-Jun-2018 |
Abstract: | [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 $\mathbb{Z^\mu}$. |
Note: | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2018, Director: Rosa Maria Miró-Roig |
URI: | http://hdl.handle.net/2445/128969 |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 289.4 kB | Adobe PDF | View/Open |
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