Holomorphic de Rham cohomology of strongly pseudoconvex CR manifolds with S-1-actions
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AbstractIn this paper, we study the holomorphic de Rham cohomology of a compact strongly pseudoconvex CR manifold X in C-N with a transversal holomorphic S-1-action. The holomorphic de Rham cohomology is derived from the Kohn-Rossi cohomology and is particularly interesting when X is of real dimension three and the Kohn-Rossi cohomology is infinite dimensional. In Theorem A, we relate the holomorphic de Rham cohomology H-h(k)(X) to the punctured local holomorphic de Rham cohomology at the singularity in the variety V which X bounds. In case X is of real codimension three in Cn+1, we prove that H-h(n-1)(X) and H-h(n)(X) have the same dimension while all other H-h(k)(X), k > 0, vanish (Theorem B). If X is three-dimensional and V has at most rational singularities, we prove that H-h(1) (X) and H-h(2) (X) vanish (Theorem C). In case X is three-dimensional and N = 3, we obtain in Theorem D a complete characterization of the vanishing of the holomorphic de Rham cohomology of X.
All Author(s) ListLuk HS, Yau SST
Journal nameJournal of Differential Geometry
Year2003
Month1
Day1
Volume Number63
Issue Number1
PublisherLEHIGH UNIV
Pages155 - 170
ISSN0022-040X
eISSN1945-743X
LanguagesEnglish-United Kingdom
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2020-28-10 at 00:11