A GKM variety is a variety $X$, often assumed to be smooth and complete, with an action of an algebraic torus $T$ satisfying the following conditions: (i) $X$ is equivariantly formal with respect to the action of $T$, (ii) $X$ has finitely many $T$-fixed points, and (iii) $X$ has finitely many one-dimensional $T$-orbits. The data of the zero and one dimensional $T$-orbits of $X$ define the moment graph of $X$, with which one can carry out $T$-equivariant cohomology and $T$-equivariant $K$-theory computations via the method of localization. This package provides methods for these computations in Macaulay2.
For mathematical background see:
The following people have contributed code, improved existing code, or enhanced the documentation: Tim Seynnaeve.
This documentation describes version 0.1 of GKMVarieties.
If you have used this package in your research, please cite it as follows:
|
The object GKMVarieties is a package, defined in GKMVarieties.m2, with auxiliary files in GKMVarieties/.
The source of this document is in GKMVarieties/Documentation_GKMVarieties.m2:57:0.