On the stability of the cohomology of complex structures
HTML articles powered by AMS MathViewer
- by Tapio Klemola PDF
- Trans. Amer. Math. Soc. 157 (1971), 87-97 Request permission
Abstract:
Let $\mathcal {V} \stackrel {\pi }{\to } M$ be a differentiable family of compact complex manifolds ${V_t} = {\pi ^{ - 1}}(t)$ on $M = \{ t \in {R^m}|\;|t| < 1\} ,\;\mathcal {B} \to \mathcal {V}$ 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 $0 \in M$.References
-
A. Froehlicher, E. Kobayashi and A. Nijenhuis, Deformation theory of complex manifolds, Lecture Notes, University of Washington, Seattle, Wash., 1957.
- Ph. A. Griffiths, The extension problem for compact submanifolds of complex manifolds. I. The case of a trivial normal bundle, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 113–142. MR 0190952
- F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. MR 0202713
- Tapio Klemola, On transportable forms, Canad. Math. Bull. 15 (1972), 93–101. MR 316758, DOI 10.4153/CMB-1972-017-x
- K. Kodaira and D. C. Spencer, On deformations of complex analytic structures. I, II, Ann. of Math. (2) 67 (1958), 328–466. MR 112154, DOI 10.2307/1970009
- K. Kodaira and D. C. Spencer, On deformations of complex analytic structures. III. Stability theorems for complex structures, Ann. of Math. (2) 71 (1960), 43–76. MR 115189, DOI 10.2307/1969879
- M. Kuranishi, New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 142–154. MR 0176496
- H. K. Nickerson, On differential operators and connections, Trans. Amer. Math. Soc. 99 (1961), 509–539. MR 162212, DOI 10.1090/S0002-9947-1961-0162212-4
- L. Nirenberg, Partial differential equations with applications in geometry, Lectures on Modern Mathematics, Vol. II, Wiley, New York, 1964, pp. 1–41. MR 0178219
Additional Information
- © Copyright 1971 American Mathematical Society
- 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