GKM variety explained

In algebraic geometry, a GKM variety is a complex algebraic variety equipped with a torus action that meets certain conditions.[1] 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]

See also

Notes and References

  1. Gonzales. Richard Paul . GKM theory of rationally smooth group embeddings. University of Western Ontario. PhD . 2011.
  2. Goresky. Mark . Kottwitz. Robert . MacPherson . Robert . Equivariant cohomology, Koszul duality, and the localization theorem. . 1998 . 131 . 25–83 . 10.1007/s002220050197 . Mark Goresky . Robert Kottwitz . Robert MacPherson (mathematician). 10.1.1.42.6450 .