Skip to main content
Book cover

Hodge Theory pp 115–124Cite as

Poincaré lemma for a variation of polarized hodge structure

Part of the Lecture Notes in Mathematics book series (LNM,volume 1246)

Keywords

  • Hodge Structure
  • Nilpotent Orbit
  • Minimal Extension
  • Hodge Decomposition
  • Mixed Hodge Structure

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   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.95
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. A. A. Beilinson, J. Bernstein and P. Deligne, Faisceaux pervers, Astérisque, 100 (1982), Soc. Math. France.

    Google Scholar 

  2. E. Cattani and A. Kaplan, Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structures, Inv. Math. 67 (1982), 101–115.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E. Cattani, A. Kaplan and W. Schmid, The SL2-orbit theorem in several variables (to appear).

    Google Scholar 

  4. E. Cattani, A. Kaplan and W. Schmid, L2 and intersection cohomologies for a polarizable variation of Hodge structure, preprint.

    Google Scholar 

  5. M. Kashiwara, The asymptotic behavior of a variation of polarized Hodge structures, Publ. of R.I.M.S., Kyoto Univ. 21 (1985), 853–875.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. M. Kashiwara and T. Kawai, The Poincaré lemma for a variation of polarized Hodge structure, Proc. Japan Acad., 61 Ser. A (1985), 164–167.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. M. Kashiwara and T. Kawai, Hodge structure and holonomic systems, Proc. Japan Acad. 62, Ser. A (1986) 1–4.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. M. Kashiwara and T. Kawai, The Poincaré lemma for variations of Hodge structure, to appear in Publ. R.I.M.S.

    Google Scholar 

  9. W. Schmid, Variation of Hodge structure: the singularities of the period mappings, Inv. Math. 22 (1973), 211–319.

    CrossRef  MATH  Google Scholar 

  10. A. Weil, Introduction à l'étude des variétés kähleriennes, Hermann, Paris, 1958.

    MATH  Google Scholar 

  11. S. Zucker, Hodge theory with degenerating coefficients, Annals of Math., 109 (1979), 415–476.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1987 Springer-Verlag

About this chapter

Cite this chapter

Kashiwara, M. (1987). Poincaré lemma for a variation of polarized hodge structure. In: Cattani, E., Kaplan, A., Guillén, F., Puerta, F. (eds) Hodge Theory. Lecture Notes in Mathematics, vol 1246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077534

Download citation

  • DOI: https://doi.org/10.1007/BFb0077534

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17743-2

  • Online ISBN: 978-3-540-47794-5

  • eBook Packages: Springer Book Archive