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DC Field | Value | Language |
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dc.contributor.author | Elías García, Joan | - |
dc.date.accessioned | 2024-07-11T07:56:06Z | - |
dc.date.available | 2024-07-11T07:56:06Z | - |
dc.date.issued | 2022-06-25 | - |
dc.identifier.issn | 1660-5446 | - |
dc.identifier.uri | http://hdl.handle.net/2445/214510 | - |
dc.description.abstract | The aim of this note is to exploit a new relationship between additive combinatorics and the geometry of monomial projective curves. We associate to a finite set of non-negative integers $A=\left\{a_1, \ldots, a_n\right\}$ a monomial projective curve $C_A \subset \mathbb{P}_{\mathbf{k}}^{n-1}$ such that the Hilbert function of $C_A$ and the cardinalities of $s A:=\left\{a_{i_1}+\cdots+a_{i_s} \mid 1 \leq i_1 \leq \cdots \leq i_s \leq n\right\}$ agree. The singularities of $C_A$ determines the asymptotic behaviour of $|s A|$, equivalently the Hilbert polynomial of $C_A$, and the asymptotic structure of $S A$. We show that some additive inverse problems can be translate to the rigidity of Hilbert polynomials and we improve an upper bound of the Castelnuovo-Mumford regularity of monomial projective curves by using results of additive combinatorics. | - |
dc.format.extent | 11 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Reproducció del document publicat a: https://doi.org/10.1007/s00009-022-02108-0 | - |
dc.relation.ispartof | Mediterranean Journal of Mathematics, 2022, vol. 19 | - |
dc.relation.uri | https://doi.org/10.1007/s00009-022-02108-0 | - |
dc.rights | cc-by (c) Joan Elias García, 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 | Successions (Matemàtica) | - |
dc.subject.classification | Corbes algebraiques | - |
dc.subject.other | Commutative algebra | - |
dc.subject.other | Sequences (Mathematics) | - |
dc.subject.other | Algebraic curves | - |
dc.title | Sumsets and projective curves | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 749375 | - |
dc.date.updated | 2024-07-11T07:56:11Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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