Equivariant Intersection Cohomology of Toric Varieties

dc.creatorBarthel, Gottfried
dc.creatorBrasselet, Jean-Paul
dc.creatorFieseler, Karl-Heinz
dc.creatorKaup, Ludger
dc.date1999-04-28
dc.date.accessioned2026-07-07T05:28:51Z
dc.date.available2026-07-07T05:28:51Z
dc.descriptionWe investigate the equivariant intersection cohomology of a toric variety. Considering the defining fan of the variety as a finite topological space with the subfans being the open sets (that corresponds to the "toric" topology given by the invariant open subsets), equivariant intersection cohomology provides a sheaf (of graded modules over a sheaf of graded rings) on that "fan space". We prove that this sheaf is a "minimal extension sheaf", i.e., that it satisfies three relatively simple axioms which are known to characterize such a sheaf up to isomorphism. In the verification of the second of these axioms, a key role is played by "equivariantly formal" toric varieties, where equivariant and "usual" (non-equivariant) intersection cohomology determine each other by Kunneth type formulae. Minimal extension sheaves can be constructed in a purely formal way and thus also exist for non-rational fans. As a consequence, we can extend the notion of an equivariantly formal fan even to this general setup. In this way, it will be possible to introduce "virtual" intersection cohomology for equivariantly formal non-rational fans.
dc.description31 pages, AMS-Latex (all "private" macros included), to be published in "Algebraic Geometry - Hirzebruch 70" (Proceedings of the conference at the Banach Centre, Warszawa, May 1998), Contemporary Mathematics, AMS
dc.identifierhttps://arxiv.org/abs/math/9904159
dc.identifierhttp://arxiv.org/abs/math/9904159
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78419
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.subjectCombinatorics
dc.subject14M25, 32S60, 52B20, 55N25
dc.titleEquivariant Intersection Cohomology of Toric Varieties
dc.typetext

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