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Transactions of the American Mathematical Society

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On the stability of the cohomology of complex structures


Author: Tapio Klemola
Journal: Trans. Amer. Math. Soc. 157 (1971), 87-97
MSC: Primary 57.60; Secondary 32.00
DOI: https://doi.org/10.1090/S0002-9947-1971-0282383-5
MathSciNet review: 0282383
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Abstract: Let $ \mathcal{V}\mathop \pi \limits_ \to M$ be a differentiable family of compact complex manifolds $ {V_t} = {\pi ^{ - 1}}(t)$ on $ M = \{ t \in {R^m}\vert\;\vert t\vert < 1\} ,\;\mathcal{B} \to \mathcal{V}$ a differentiable family of holomorphic vector bundles $ {B_t} \to {V_t},t \in M$. In this paper we study conditions for the cohomology groups $ H_{\bar \partial t}^{r,s}({B_t})$ to be constant in a neighborhood of $ 0 \in M$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0282383-5
Keywords: Complex manifolds, deformation
Article copyright: © Copyright 1971 American Mathematical Society

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