Abstract
The aim of these lectures is to give an introduction to the theory of deformations of complex structures as developed by Kodaira and Spencer. The theory studies complex structures which are near a given complex structure on a compact differentiable manifold. One also has an analogous theory of deformations of holomorphic vector bundles on a compact complex manifold.
Keywords
- Vector Field
- Vector Bundle
- Complex Manifold
- Compact Riemann Surface
- Continuous Linear Operator
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References
K. Kodaira and D.C. Spencer: On deformations of complex analytic structures I,II. Annals of Mathematics, 67(1958), 328–466.
K. Kodaira and D.C. Spencer: A theorem of completeness for analytic fibre spaces Acta Math. 100(1958), 281–294.
K. Kodaira, L. Nirenberg and D.C. Spencer: On the existence of deformations of complex analytic structures, Ann. of Math. 68(1958), 450–459.
K. Kodaira and D.C. Spencer: On deformations of complex analytic structures III, Ann. of Math. 71(1960), 43–76.
M.S. Narasimhan and C.S. Seshadri: Stable and unitary vector bundles on a Compact Riemann surface, Ann. of Math. 82(1965), 540–567.
M.S. Narasimhan and R.R. Simha: Manifolds with ample canonical class, Inventiones Math. 5(1968), 120–128.
Y.T. Siu: Dimensions of sheaf cohomology groups under holomorphic deformation, Math. Ann. 192(1971), 203–215.
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© 1982 Springer-Verlag Berlin Heidelberg
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Narasimhan, M.S. (1982). Deformations of Complex Structures and Holomorphic Vector Bundles. In: Complex Analysis. Lecture Notes in Mathematics, vol 950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061878
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DOI: https://doi.org/10.1007/BFb0061878
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11596-0
Online ISBN: 978-3-540-39366-5
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