Skip to main content
SpringerLink
Log in

Schubert varieties are arithmetically Cohen-Macaulay

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. DeConcini, C., Lakshmibai, V.: Arithmetic Cohen-Macaulayness and arithmetic normality for Schubert varieties. Am. J. Math.103, 835–850 (1981)

    Google Scholar 

  2. Demazure, M.: Désingularisation des variétés de Schubert généralisées. Ann. Sc. E.N.S.7, 53–88 (1974)

    Google Scholar 

  3. Hartshorne, R.: Algebraic geometry. Graduate Texts Math. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  4. Hochster, M.: Grassmannians and their Schubert varieties are arithmetically Cohen-Macaulay. J. Algebra25, 40–57 (1973)

    Google Scholar 

  5. Huneke, C., Lakshmibai, V.: Cohen-Macaulayness and normality of the multi-cones over Schubert varieties inSL(n)/B (Preprint)

  6. Kempf, G.: Vanishing theorems for flag manifolds. Am. J. Math.98, 325–331 (1976)

    Google Scholar 

  7. Kempf, G.: Linear systems on homogeneous spaces. Ann. Math.103, 557–591 (1976)

    Google Scholar 

  8. Kempf, G. et al.: Toroidal Embeddings. Lect. Notes Math.339. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  9. Lakshmibai, V., Seshadri, C.S.: Geometry ofG/P-V. (To appear in Ann. Sci. E.N.S. 1985)

  10. Laksov, D.: The arithmetic Cohen-Macaulay character of Schubert schemes. Acta Math.129, 1–9 (1972)

    Google Scholar 

  11. Mehta, V.B., Ramanathan, A.: Frobenius splitting and cohomology vanishing for Schubert varieties. (To appear in Ann. Math. 1985)

  12. Musili, C.: Postulation formula for Schubert varieties. J. Indian Math. Soc.36, 143–171 (1972)

    Google Scholar 

  13. Ramanan, S., Ramanathan, A.: Projective normality of flag varieties and Schubert varieties. Invent. Math.79, 217–224 (1985)

    Google Scholar 

  14. Ramanathan, A.: Equations defining Schubert varieties and Frobenius splitting of the diagonal. (Preprint)

  15. Musili, C., Seshadri, C.S.: Schubert varieties and the variety of complexes. In: Arithmetic and Geometry. Volume dedicated to I.R. Shaferavich.2, pp. 329–359. Boston: Birkhauser 1983

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005, Bombay, India

    A. Ramanathan

Authors
  1. A. Ramanathan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ramanathan, A. Schubert varieties are arithmetically Cohen-Macaulay. Invent Math 80, 283–294 (1985). https://doi.org/10.1007/BF01388607

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388607

Keywords

Search

Navigation