Equivariant Intersection Cohomology of Toric Varieties
| dc.creator | Barthel, Gottfried | |
| dc.creator | Brasselet, Jean-Paul | |
| dc.creator | Fieseler, Karl-Heinz | |
| dc.creator | Kaup, Ludger | |
| dc.date | 1999-04-28 | |
| dc.date.accessioned | 2026-07-07T05:28:51Z | |
| dc.date.available | 2026-07-07T05:28:51Z | |
| dc.description | We 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.description | 31 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.identifier | https://arxiv.org/abs/math/9904159 | |
| dc.identifier | http://arxiv.org/abs/math/9904159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78419 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | Combinatorics | |
| dc.subject | 14M25, 32S60, 52B20, 55N25 | |
| dc.title | Equivariant Intersection Cohomology of Toric Varieties | |
| dc.type | text |