Rational smoothness, cellular decompositions and GKM theory

Abstract

We introduce the notion of Q-filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main results develop GKM theory in this setting. We also supply a method for building nice combinatorial bases on the equivariant cohomology of any Q-filtrable GKM variety. Applications to the theory of group embeddings are provided.

27 pages, minor changes in the exposition

References in corpus (1)

• The orbifold Chow ring of toric Deligne-Mumford stacks

Cited by in corpus (2)

• GKM theory for orbifold stratified spaces and application to singular toric varieties
• Desingularizations of Quiver Grassmannians for the Equioriented Cycle Quiver