Geometry & Topology
- Geom. Topol.
- Volume 18, Number 1 (2014), 291-326.
Rational smoothness, cellular decompositions and GKM theory
We introduce the notion of –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 –filtrable GKM variety. Applications to the theory of group embeddings are provided.
Geom. Topol., Volume 18, Number 1 (2014), 291-326.
Received: 15 July 2012
Revised: 19 August 2013
Accepted: 20 September 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Secondary: 55N91: Equivariant homology and cohomology [See also 19L47] 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Gonzales, Richard. Rational smoothness, cellular decompositions and GKM theory. Geom. Topol. 18 (2014), no. 1, 291--326. doi:10.2140/gt.2014.18.291. https://projecteuclid.org/euclid.gt/1513732724