Skip to main content

Deformations of Complex Structures and Holomorphic Vector Bundles

  • Conference paper

Part of the Lecture Notes in Mathematics book series (LNM,volume 950)

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

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Kodaira and D.C. Spencer: On deformations of complex analytic structures I,II. Annals of Mathematics, 67(1958), 328–466.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. K. Kodaira and D.C. Spencer: A theorem of completeness for analytic fibre spaces Acta Math. 100(1958), 281–294.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. K. Kodaira, L. Nirenberg and D.C. Spencer: On the existence of deformations of complex analytic structures, Ann. of Math. 68(1958), 450–459.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. K. Kodaira and D.C. Spencer: On deformations of complex analytic structures III, Ann. of Math. 71(1960), 43–76.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. M.S. Narasimhan and C.S. Seshadri: Stable and unitary vector bundles on a Compact Riemann surface, Ann. of Math. 82(1965), 540–567.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. M.S. Narasimhan and R.R. Simha: Manifolds with ample canonical class, Inventiones Math. 5(1968), 120–128.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Y.T. Siu: Dimensions of sheaf cohomology groups under holomorphic deformation, Math. Ann. 192(1971), 203–215.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • 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

  • eBook Packages: Springer Book Archive