Groebner and diagonal bases in Orlik-Solomon type algebras

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dc.creatorCordovil, Raul
dc.creatorForge, David
dc.date2001-06-11
dc.date2003-10-07
dc.date.accessioned2026-07-07T04:42:06Z
dc.date.available2026-07-07T04:42:06Z
dc.descriptionThe Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal I(M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the Orlik-Solomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, called X-algebras, are considered. These new algebras include, apart from the Orlik-Solomon algebras, the Orlik-Solomon-Terao algebra of a set of vectors and the Cordovil algebra of an oriented matroid. To encode an important property of the "no broken circuit bases" of the Orlik-Solomon-Terao algebras, Andras Szenes has introduced a particular type of bases, the so called "diagonal bases". This notion extends naturally to X-algebras. We give a survey of the results obtained by the authors concerning the construction of Groebner bases of I(M) and diagonal bases of Orlik-Solomon type algebras and we present the combinatorial analogue of an ``iterative residue formula'' introduced by Szenes.
dc.description15 pages, Latex, 1 figure, to appear in Cubo Journal
dc.identifierhttps://arxiv.org/abs/math/0106082
dc.identifierhttp://arxiv.org/abs/math/0106082
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61629
dc.subjectAlgebraic Topology
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject05B35; 52C35; 14F40
dc.titleGroebner and diagonal bases in Orlik-Solomon type algebras
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