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DC Field | Value | Language |
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dc.contributor.author | Colarte Gómez, Liena | - |
dc.contributor.author | Elías García, Joan | - |
dc.contributor.author | Miró-Roig, Rosa M. (Rosa Maria) | - |
dc.date.accessioned | 2023-02-03T09:06:50Z | - |
dc.date.available | 2023-02-03T09:06:50Z | - |
dc.date.issued | 2022-03-28 | - |
dc.identifier.issn | 0010-0757 | - |
dc.identifier.uri | http://hdl.handle.net/2445/193020 | - |
dc.description.abstract | In this paper, to any subset $\mathcal{A} \subset \mathbb{Z}^n$ we explicitly associate a unique monomial projection $Y_{n, d_{\mathcal{A}}}$ of a Veronese variety, whose Hilbert function coincides with the cardinality of the $t$-fold sumsets $t \mathcal{A}$. This link allows us to tackle the classical problem of determining the polynomial $p_{\mathcal{A}} \in \mathbb{Q}[t]$ such that $|t \mathcal{A}|=p_{\mathcal{A}}(t)$ for all $t \geq t_0$ and the minimum integer $n_0(\mathcal{A}) \leq t_0$ for which this condition is satisfied, i.e. the so-called phase transition of $|t \mathcal{A}|$. We use the Castelnuovo-Mumford regularity and the geometry of $Y_{n, d_{\mathcal{A}}}$ to describe the polynomial $p_{\mathcal{A}}(t)$ and to derive new bounds for $n_0(\mathcal{A})$ under some technical assumptions on the convex hull of $\mathcal{A}$; and vice versa we apply the theory of sumsets to obtain geometric information of the varieties $Y_{n, d_{\mathcal{A}}}$. | - |
dc.format.extent | 22 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1007/s13348-022-00352-x | - |
dc.relation.ispartof | Collectanea Mathematica, 2022 | - |
dc.relation.uri | https://doi.org/10.1007/s13348-022-00352-x | - |
dc.rights | cc by (c) Liena Colarte Gómez et al., 2022 | - |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Àlgebra commutativa | - |
dc.subject.classification | Teoria de nombres | - |
dc.subject.other | Commutative algebra | - |
dc.subject.other | Number theory | - |
dc.title | Sumsets and Veronese varieties | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 719114 | - |
dc.date.updated | 2023-02-03T09:06:50Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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