GKM variety

In algebraic geometry, a GKM variety is a complex algebraic variety equipped with a torus action that meets certain conditions.^[1]^{: Def. 1.4.13} The concept was introduced by Mark Goresky, Robert Kottwitz, and Robert MacPherson in 1998.^[2] The torus action of a GKM variety must be skeletal: both the set of fixed points of the action, and the number of one-dimensional orbits of the action, must be finite. In addition, the action must be equivariantly formal, a condition that can be phrased in terms of the torus' rational cohomology.^[1]^{: Def. 1.4.1}

References

^ ^a ^b Gonzales, Richard Paul (2011). GKM theory of rationally smooth group embeddings (PhD). University of Western Ontario.
^ Goresky, Mark; Kottwitz, Robert; MacPherson, Robert (1998). "Equivariant cohomology, Koszul duality, and the localization theorem" (PDF). Inventiones mathematicae. 131: 25–83. CiteSeerX 10.1.1.42.6450. doi:10.1007/s002220050197.

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[Gonzales-1] Gonzales, Richard Paul (2011). GKM theory of rationally smooth group embeddings (PhD). University of Western Ontario.

[GKM-2] Goresky, Mark; Kottwitz, Robert; MacPherson, Robert (1998). "Equivariant cohomology, Koszul duality, and the localization theorem" (PDF). Inventiones mathematicae. 131: 25–83. CiteSeerX 10.1.1.42.6450. doi:10.1007/s002220050197.

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References