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A Generalisation of Nagata's Theorem on Ruled Surfaces

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Compositio Mathematica

Abstract

We prove a generalisation of a theorem of Nagata on ruled surface to the case of the fiber bundle E/P → X, associated to a principal G-bundle E. Using this we prove boundedness for the isomorphism classes of semi-stable G-bundles in all characteristics.

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References

  1. Grothendieck, A.: Fondements de la géométrie algébrique, Séminaire Bourbaki, Secretariat Mathematique, Paris, 1962.

    Google Scholar 

  2. Grothendieck, A. and Dieudonné, J.: Elements de géométrie algébriques I, 1960.

  3. Ramanathan, A.: Moduli for principal bundles over algebraic curves I. Proc. Indian Acad. Sci. (Math. Sci.), 106(3) (1997), 301-328.

    Google Scholar 

  4. Ramanathan, A.: Moduli for principal bundles over algebraic curves II. Proc. Indian Acad. Sci. (Math. Sci.), 106(4) (1997), 421-449.

    Google Scholar 

  5. Mumford, D.: Abelian Varieties, Oxford Univ. Press, Oxford, 1970.

    Google Scholar 

  6. Harder, G.: Halbeinfache Gruppenschemate über völlstandigen Kurven, Invent. Math. 6 (1968), 107-149.

    Google Scholar 

  7. Lange, H.: Some geometrical aspects of vectorbundles on curves, Aportaciones Mat. 5 (1992) 53-72.

    Google Scholar 

  8. Nagata, M.: On self-intersection number of a section on a ruled surface, Nagoya Math. J. 37 (1970) 191-196.

    Google Scholar 

  9. Nitsure, N.: Boundedness for the moduli of G-bundles for classical groups, Algebraic Geometry Preprint (9802090), 1998.

  10. Itaka, S.: Algebraic Geometry, Springer-Verlag, Berlin, 1982.

    Google Scholar 

  11. Mori, S.: Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979), 593-606.

    Google Scholar 

  12. Mukai, S. and Sakai, F.: Maximal sub-bundles of a vector bundles on a curve, Manuscripta Math. 52 (1985), 251-256.

    Google Scholar 

  13. Ramanan, S.: Orthogonal and spin bundles over hyperelliptic curves, Proc. Indian Acad. Sci. 90(2) (1981), 151-166.

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai, 400 005, India

    Yogish I. Holla

  2. ICTP, PO Box 586, Strada Costiera 11, Miramare, I-34100, Italy

    M. S. Narasimhan

Authors
  1. Yogish I. Holla
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  2. M. S. Narasimhan
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Holla, Y.I., Narasimhan, M.S. A Generalisation of Nagata's Theorem on Ruled Surfaces. Compositio Mathematica 127, 321–332 (2001). https://doi.org/10.1023/A:1017505213601

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