Skip to main content

Some remarks on L2 and intersection cohomologies

  • 915 Accesses

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

Keywords

  • Spectral Sequence
  • Hodge Structure
  • Zariski Open Subset
  • Mixed Hodge Structure
  • Intersection Cohomology

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. Borel et al.: Intersection cohomology. Progress in Math. 50 (1984), Birkhäuser, Boston.

    Google Scholar 

  2. A. Borel and W. Casselman: Cohomologie d'intersection et L2-cohomologie de variétés arithmétiques de rang rationnel 2. C. R. Acad. Sc. Paris, 301, Série I, 369–373 (1985).

    MathSciNet  MATH  Google Scholar 

  3. E. Cattani, A. Kaplan and W. Schmid: Degeneration of Hodge structures. Ann. of Math. 123, 457–535 (1986).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. E. Cattani, A. Kaplan and W. Schmid: L2 and intersection cohomologies for a polarized variation of Hodge structure. Invent. math. To appear.

    Google Scholar 

  5. E. Cattani, A. Kaplan and W. Schmid: Variations of polarized Hodge structure: asymptotics and monodromy. This volume.

    Google Scholar 

  6. J. Cheeger: On the Hodge theory of Riemannian pseudomanifolds. Proc. Symp. Pure Math. AMS 36, 91–146 (1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. J. Cheeger, M. Goresky and R. MacPherson: L2-cohomology and intersection homology for singular algebraic varieties. In: Seminar on Differential Geometry, S.-T. Yau, ed., 303–340. Princeton Univ. Press, (1982).

    Google Scholar 

  8. M. Cornalba and P. Griffiths: Analytic cycles and vector bundles on non compact algebraic varieties. Invent. math. 28, 1–106 (1975).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. P. Deligne: Personal communication, dated January 16, 1981.

    Google Scholar 

  10. M. Goresky and R. MacPherson: Intersection homology, II, Invent. math. 71, 77–129 (1983).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. W.-C. Hsiang and V. Pati: L2-cohomology of normal algebraic surfaces, I. Invent. math. 81, 395–412 (1985).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. M. Kashiwara: Poincaré lemma for a variation of polarized Hodge structure. This volume.

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. M. Saito: Modules de Hodge polarisables. Preprint.

    Google Scholar 

  15. L. Saper: L2-cohomology and intersection homology of certain algebraic varieties with isolated singularities. Invent. math. 82, 207–255 (1985).

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. S. Zucker: Hodge theory with degenerating coefficients: L2-cohomology in the Poincaré metric. Ann. of Math. 109, 415–476 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. S. Zucker: L2-cohomology of warped products and arithmetic groups. Invent. math. 70, 169–218 (1982).

    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

Cattani, E., Kaplan, A., Schmid, W. (1987). Some remarks on L2 and intersection cohomologies. 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/BFb0077527

Download citation

  • DOI: https://doi.org/10.1007/BFb0077527

  • 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