On localization in holomorphic equivariant cohomology
Ugo Bruzzo, Vladimir Rubtsov
TL;DR
This paper establishes a new localization formula in holomorphic equivariant cohomology, extending several classical formulas in complex geometry and equivariant theory.
Contribution
It generalizes existing localization formulas to the setting of holomorphic equivariant cohomology associated with Atiyah algebroids.
Findings
Proves a localization formula for holomorphic equivariant cohomology.
Extends classical localization formulas by Feng-Ma, Carrell-Liebermann, Baum-Bott, and K. Liu.
Provides a unified framework for localization in complex geometry.
Abstract
We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Holomorphic and Operator Theory