Rational smoothness, cellular decompositions and GKM theory
Richard Gonzales
TL;DR
This paper introduces Q-filtrable varieties with rationally smooth cells, extends GKM theory to this setting, and provides methods for constructing combinatorial bases in equivariant cohomology, with applications to group embeddings.
Contribution
It develops GKM theory for Q-filtrable varieties and offers a new method for building bases in equivariant cohomology, advancing the understanding of these geometric structures.
Findings
Q-filtrable varieties have rationally smooth cells
GKM theory is extended to Q-filtrable varieties
A method for constructing combinatorial bases is provided
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.