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http://hdl.handle.net/2445/190625
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DC Field | Value | Language |
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dc.contributor.author | Colarte Gómez, Liena | - |
dc.contributor.author | Mezzetti, Emilia | - |
dc.contributor.author | Miró-Roig, Rosa M. (Rosa Maria) | - |
dc.date.accessioned | 2022-11-09T09:08:46Z | - |
dc.date.available | 2022-11-09T09:08:46Z | - |
dc.date.issued | 2021-01-06 | - |
dc.identifier.issn | 0373-3114 | - |
dc.identifier.uri | http://hdl.handle.net/2445/190625 | - |
dc.description.abstract | Given any diagonal cyclic subgroup $\Lambda \subset G L(n+1, k)$ of order $d$, let $I_d \subset k\left[x_0, \ldots, x_n\right]$ be the ideal generated by all monomials $\left\{m_1, \ldots, m_r\right\}$ of degree $d$ which are invariants of $\Lambda . I_d$ is a monomial Togliatti system, provided $r \leq\left(\begin{array}{c}d+n-1 \\ n-1\end{array}\right)$, and in this case the projective toric variety $X_d$ parameterized by $\left(m_1, \ldots, m_r\right)$ is called a $G T$-variety with group $\Lambda$. We prove that all these $G T$-varieties are arithmetically Cohen-Macaulay and we give a combinatorial expression of their Hilbert functions. In the case $n=2$, we compute explicitly the Hilbert function, polynomial and series of $X_d$. We determine a minimal free resolution of its homogeneous ideal and we show that it is a binomial prime ideal generated by quadrics and cubics. We also provide the exact number of both types of generators. Finally, we pose the problem of determining whether a surface parameterized by a Togliatti system is aCM. We construct examples that are aCM and examples that are not. | - |
dc.format.extent | 24 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1007/s10231-020-01058-2 | - |
dc.relation.ispartof | Annali di Matematica Pura ed Applicata, 2021, vol. 200, p. 1757-1780 | - |
dc.relation.uri | https://doi.org/10.1007/s10231-020-01058-2 | - |
dc.rights | (c) Springer Verlag, 2021 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Varietats algebraiques | - |
dc.subject.classification | Anells commutatius | - |
dc.subject.classification | Mòduls de Cohen-Macaulay | - |
dc.subject.classification | Grups algebraics diferencials | - |
dc.subject.other | Algebraic varieties | - |
dc.subject.other | Commutative rings | - |
dc.subject.other | Cohen-Macaulay modules | - |
dc.subject.other | Differential algebraic groups | - |
dc.title | On the arithmetic Cohen-Macaulayness of varieties parameterized by Togliatti systems | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 709646 | - |
dc.date.updated | 2022-11-09T09:08:46Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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709646.pdf | 323.01 kB | Adobe PDF | View/Open |
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