Rational smoothness, cellular decompositions and GKM theory

Richard Gonzales

doi:10.2140/gt.2014.18.291

Rational smoothness, cellular decompositions and GKM theory

Richard Gonzales

Sabancı Üniversitesi

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 Białynicki-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.

Original language	English
Pages (from-to)	291-326
Number of pages	36
Journal	Geometry and Topology
Volume	18
Issue number	1
DOIs	https://doi.org/10.2140/gt.2014.18.291
State	Published - 29 Jan 2014
Externally published	Yes

Keywords

Algebraic monoids
Algebraic torus actions
Equivariant cohomology
GKM theory
Group embeddings
Rational smoothness

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AB - 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 Białynicki-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.

KW - Algebraic monoids

KW - Algebraic torus actions

KW - Equivariant cohomology

KW - GKM theory

KW - Group embeddings

KW - Rational smoothness

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JO - Geometry and Topology

JF - Geometry and Topology

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Rational smoothness, cellular decompositions and GKM theory

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Keywords

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