Background cohomology of a non-compact Kähler 𝐺-manifold

Braverman, Maxim

doi:10.1090/S0002-9947-2014-06314-9

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
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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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