Specializations of multigradings and the arithmetical rank of lattice ideals

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dc.creatorKatsabekis, Anargyros
dc.creatorThoma, Apostolos
dc.date2008-11-24
dc.date2009-05-08
dc.date.accessioned2026-07-07T13:12:27Z
dc.date.available2026-07-07T13:12:27Z
dc.descriptionIn this article we study specializations of multigradings and apply them to the problem of the computation of the arithmetical rank of a lattice ideal $I_{L_{\mathcal{G}}} \subset K[x_{1},...,x_{n}]$. The arithmetical rank of $I_{L_{\mathcal{G}}}$ equals the $\mathcal{F}$-homogeneous arithmetical rank of $I_{L_{\mathcal{G}}}$, for an appropriate specialization $\mathcal{F}$ of $\mathcal{G}$. To the lattice ideal $I_{L_{\mathcal{G}}}$ and every specialization $\mathcal{F}$ of $\mathcal{G}$ we associate a simplicial complex. We prove that combinatorial invariants of the simplicial complex provide lower bounds for the $\mathcal{F}$-homogeneous arithmetical rank of $I_{L_{\mathcal{G}}}$.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0811.3830
dc.identifierhttp://arxiv.org/abs/0811.3830
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229585
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject14M25;13F55
dc.titleSpecializations of multigradings and the arithmetical rank of lattice ideals
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