Skip to main content

Cohomology of the complement to an elliptic arrangement

  • Conference paper
Configuration Spaces

Part of the book series: CRM Series ((CRMSNS))

Abstract

We consider the complement to an arrangement of hyperplanes in a cartesian power of an elliptic curve and describe its cohomology with coefficients in a nontrivial rank one local system.

Supported in part by AG Laboratory GU-HSE, RF government grant, ag. 11 11.G34.31.0023.

Supported in part by NSF grant DMS-1101508.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 24.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 34.95
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. I. Arnold, The cohomology ring of the pure braid group, Mat. Zametki 5 (1969), 227-231, Math. Notes 5 (1969) 138–140.

    Article  Google Scholar 

  2. G. Felder and A. Varchenko, Integral representation of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations, Int. Math. Res. Notices n. 5(1995), 221–233.

    Google Scholar 

  3. G. Felder and A. Varchenko Three formulae for eigenfunctions of integrable Schrödinger operators, Compositio Math. 107 (1997), 143–175.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Felder, R. Rimányi and A. Varchenko, Poincaré-Birkhoff-Witt expansions of the canonical elliptic differential form, In: “Quantum Groups”, 191–208, Contemp. Math., Vol. 433, Amer. Math. Soc., Providence, RI, 2007.

    Google Scholar 

  5. P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), 167–189.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Orlik and H. Terao, “Arrangements of Hyperplanes” Springer-Verlag, Berlin-Heidelberg-New York, 1992.

    Book  Google Scholar 

  7. V. Schechtman and A. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math., (1) 106 (1991), 139–194.

    Article  MATH  MathSciNet  Google Scholar 

  8. E. B. Vinberg, “A Course in Algebra”, AMS, 2003

    Google Scholar 

  9. E. T. Whittaker and G. N. Watson, “A Course of Modern Analysis”, Reprint of the fourth (1927) edition, Cambridge University Press (September 1996).

    Google Scholar 

Download references

Authors

Editor information

A. Bjorner F. Cohen C. De Concini C. Procesi M. Salvetti

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Scuola Normale Superiore Pisa

About this paper

Cite this paper

Levin, A., Varchenko, A. (2012). Cohomology of the complement to an elliptic arrangement. In: Bjorner, A., Cohen, F., De Concini, C., Procesi, C., Salvetti, M. (eds) Configuration Spaces. CRM Series. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-431-1_17

Download citation

Publish with us

Policies and ethics