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Title: | Minimal set of binomial generators for certain Veronese 3-fold projections |
Author: | Colarte Gómez, Liena Miró-Roig, Rosa M. (Rosa Maria) |
Keywords: | Anells commutatius Varietats tòriques Geometria algebraica Geometria diferencial Commutative rings Toric varieties Algebraic geometry Differential geometry |
Issue Date: | Feb-2020 |
Publisher: | Elsevier B.V. |
Abstract: | The goal of this paper is to explicitly describe a minimal binomial generating set of a class of lattice ideals, namely the ideal of certain Veronese 3 -fold projections. More precisely, for any integer $d \geq 4$ and any $d$-th root $e$ of 1 we denote by $X_d$ the toric variety defined as the image of the morphism $\varphi_{T_d}: \mathbb{P}^3 \longrightarrow \mathbb{P}^{\mu\left(T_d\right)-1}$ where $T_d$ are all monomials of degree $d$ in $k[x, y, z, t]$ invariant under the action of the diagonal matrix $M\left(1, e, e^2, e^3\right)$. In this work, we describe a $\mathbb{Z}$-basis of the lattice $L_\eta$ associated to $I\left(X_d\right)$ as well as a minimal binomial set of generators of the lattice ideal $I\left(X_d\right)=I_{+}(\eta)$. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.jpaa.2019.06.009 |
It is part of: | Journal of Pure and Applied Algebra, 2020, vol. 224, num. 2, p. 768-788 |
URI: | http://hdl.handle.net/2445/194900 |
Related resource: | https://doi.org/10.1016/j.jpaa.2019.06.009 |
ISSN: | 0022-4049 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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