GKM_variety

GKM variety

GKM variety

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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 

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References

  1. [1]
    Gonzales, Richard Paul (2011). GKM theory of rationally smooth group embeddings (PhD). University of Western Ontario.
  2. [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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