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- W1562702765 abstract "In this paper, we study the holomorphic de Rham cohomology of a compact strongly pseudoconvex CR manifold X in ℂN with a transversal holomorphic S1-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 Hkh(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 Hn−1h(X) and Hnh(X) have the same dimension while all other Hkh(X), k > 0, vanish (Theorem B). If X is three-dimensional and V has at most rational singularities, we prove that H1h(X) and H2h(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." @default.
- W1562702765 created "2016-06-24" @default.
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- W1562702765 date "2003-01-01" @default.
- W1562702765 modified "2023-09-25" @default.
- W1562702765 title "Holomorphic De Rham Cohomology of Strongly Pseudoconvex CR Manifolds with S1-actions" @default.
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- W1562702765 doi "https://doi.org/10.4310/jdg/1080835661" @default.
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