Mathematische Annalen

, Volume 258, Issue 3, pp 213–224

Semistable sheaves on projective varieties and their restriction to curves

  • V. B. Mehta
  • A. Ramanathan
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Altman, A., Kleiman, S.: Introduction to Grothendieck duality theory. Lecture Notes in MathematicsVol. 146. Berlin, Heidelberg, New York: Springer 1970Google Scholar
  2. 2.
    Bourbaki, N.: Eléments de mathématique. Algèbre commutative, Chap. 7. Paris: Hermann 1965Google Scholar
  3. 3.
    Grothendieck, A.: Technique de descente et théorèmes d'existence en géometrié algèbrique. IV. Les schémas de Hilbert. Séminaire Bourbaki 1960/61, exposé 221Google Scholar
  4. 4.
    Grothendieck, A., Dieudonné, J.: Elément de géométrie algébriques, IV/3, IV/4. In: Publ. Math. I.H.E.S.28 (1966);32 (1967) (cited EGA)Google Scholar
  5. 5.
    Harder, G., Narasimhan, M.S.: On the cohomology groups of moduli spaces of vector bundles on curves. Math. Ann.212, 215–248 (1975)Google Scholar
  6. 6.
    Hartshorne, R.: Algebraic geometry. Graduate Texts in Mathematics, Vol. 52. Berlin, Heidelberg, New York: Springer 1977Google Scholar
  7. 7.
    Langton, S.: Valuative criteria for families of vector bundles on algebraic varieties. Ann. Math.101, 88–110 (1975)Google Scholar
  8. 8.
    Maruyama, M.: Openness of a family of torsion free sheaves. J. Math. Kyoto Univ.16, 627–637 (1976)Google Scholar
  9. 9.
    Maruyama M.: The theorem of Grauert-Mullich-Spindler. Math. Ann.255, 317–333 (1981)Google Scholar
  10. 10.
    Mumford, D.: Lectures on curves on an algebraic surface. Princeton: Princeton University Press 1966Google Scholar
  11. 11.
    Mumford, D.: Abelian varieties. Bombay: Oxford University Press 1974Google Scholar
  12. 12.
    Narasimhan, M.S., Ramanathan, A.: Openness of the semistability condition (preprint)Google Scholar
  13. 13.
    Narasimhan, M.S., Seshadri C.S.: Stable and unitary bundles on compact Riemann surfaces. Ann. Math.82, 540–567 (1965)Google Scholar
  14. 14.
    Okonek, C., Schneider, M., Spindler, H.: Vector bundles on complex projective spaces. Progress in Mathematics, Vol. 3. Basel: Birkhäuser 1980Google Scholar
  15. 15.
    Ramanan S., Ramanathan, A.: Some remarks on the instability flag (preprint)Google Scholar
  16. 16.
    Weil, A.: Sur les critères d'equivalence en géométrie algébrique. Math. Ann.128, 95–127. Also in: Collected Works Vol. II, pp. 127–159. Berlin, Heidelberg, New York: Springer 1979Google Scholar
  17. 17.
    Zariski, O.: Introduction to the problem of minimal models in the theory of algebraic surfaces. The Mathematical Society of Japan 1958Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • V. B. Mehta
    • 1
  • A. Ramanathan
    • 2
  1. 1.Center of Advanced Study in MathematicsUniversity of BombayBombayIndia
  2. 2.School of MathematicsTata Institute of Fundamental ResearchBombayIndia

Personalised recommendations