Background cohomology of a non-compact Kähler -manifold
Author:
Maxim Braverman
Journal:
Trans. Amer. Math. Soc. 367 (2015), 2235-2262
MSC (2010):
Primary 32L10
DOI:
https://doi.org/10.1090/S0002-9947-2014-06314-9
Published electronically:
July 18, 2014
MathSciNet review:
3286513
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: For a compact Lie group we define a regularized version of the
Dolbeault cohomology of a -equivariant holomorphic vector bundle over non-compact Kähler manifolds. The new cohomology is infinite dimensional, but as a representation of
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.
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Additional Information
Maxim Braverman
Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
DOI:
https://doi.org/10.1090/S0002-9947-2014-06314-9
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.
Article copyright:
© Copyright 2014
American Mathematical Society