Background cohomology of a non-compact Kähler $G$-manifold
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Abstract:
For a compact Lie group $G$ we define a regularized version of the Dolbeault cohomology of a $G$-equivariant holomorphic vector bundle over non-compact Kähler manifolds. The new cohomology is infinite dimensional, but as a representation of $G$ it decomposes into a sum of irreducible components, each of which appears in it with finite multiplicity. Thus equivariant Betti numbers are well defined. We study various properties of the new cohomology and prove that it satisfies a Kodaira-type vanishing theorem.References
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Additional Information
- Maxim Braverman
- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- MR Author ID: 368038
- Received by editor(s): April 8, 2012
- Received by editor(s) in revised form: February 21, 2013, and October 10, 2013
- Published electronically: July 18, 2014
- Additional Notes: This research was supported in part by the NSF grant DMS-1005888.
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 2235-2262
- MSC (2010): Primary 32L10
- DOI: https://doi.org/10.1090/S0002-9947-2014-06314-9
- MathSciNet review: 3286513