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Abstract

We classify principal bundles on a compact Riemann surface. A moduli space for semistable principal bundles with a reductive structure group is constructed using Mumford’s geometric invariant theory.

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References

  1. Artin M, Grothendieck Topologies Notes on a seminar by M Artin (Spring 1962), Harvard University

  2. Borel A,Linear Algebraic Groups (1969) (New York: WA Benjamin Inc.)

    MATH  Google Scholar 

  3. Borel A and Tits J, Groupes Reductifs,Pub. Math. I.H.E.S. No. 27 (1965) 55–150

  4. Grothendieck A, Technique de descente et théorèmes d’existence en géométrie algébrique, I to IV (Bourbabi exposés No. 190, 195, 212, 221, 232 and 236). Also in: Fondements de la géométrie algébrique. Secrétariat Mathematique Paris (1962). Cited as TDTE I,..., VI

  5. Grothendieck A, Techniques de construction on géométrie analytic IX: Quelques problèmes de modules. Exposé 16 in Séminaire Henri Cartan 1960/61, Fascicule 2, Secrétariat Mathematique, Paris (1962)

  6. Grothendieck A and Dieudonné J, Elements de géométrie algébriques, II, III1, and IV2.Pub. Math. I.H.E.S. No. 8, 11 and 24. Cited EGA II

  7. Grothendieck Aet al, Séminaire de géométrie algébrique, 1 and 3, Springer Verlag. Cited SGA 1

  8. Hochster M and Roberts J L, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay.Adv. Math. 13(1974) 115–175

    Article  MATH  MathSciNet  Google Scholar 

  9. Kodaira K, A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds,Ann. Math. 75 (1962) 146–162

    Article  MathSciNet  Google Scholar 

  10. Mumford D,Geometric invariant theory (1965) (Berlin-Heidelberg-New York: Springer)

    MATH  Google Scholar 

  11. Mumford D,Lectures on curves on an algebraic surface (1966) (Princeton, New Jersey: Princeton University Press)

    MATH  Google Scholar 

  12. Mumford D and Suominen K, Introduction to the theory of Moduli, in: Algebraic geometry, Oslo 1970, (F. Oort. editor) 171–222. Wolters-Noordhoff Publishing Groningen, The Netherlands, 1972

    Google Scholar 

  13. Narasimhan M S and Seshadri C S, Stable and unitary vector bundles on a compact Riemann surface.Ann. Math. 82 (1965) 540–567

    Article  MathSciNet  Google Scholar 

  14. Ramanathan A, Stable principal bundles on a compact Riemann surface,Math. Ann. 213 (1975) 129–152

    Article  MATH  MathSciNet  Google Scholar 

  15. Raynaud M, Families de fibrés vectoriels sur une surface de Riemann (D’aprés C S Seshadri, M S Narasimhan et D Mumford). Séminaire Bourbaki, Exposé 316 (1966)

    Google Scholar 

  16. Richardson R, Compact real forms of a complex semi-simple Lie algebra.J. Differ. Geo. 2(4) (1968) 411–419

    Google Scholar 

  17. Serre J P, Espaces fibrés algébriques. in:Anneaux de Chow et Applications (1958) Séminaire Chevalley

  18. Serre J P, Lie algebras and Lie groups. 1964 Lectures given at Harvard University (1965) (New York, Amsterdam: W A Benjamin Inc.)

    Google Scholar 

  19. Seshadri C S, Space of unitary vector bundles on a compact Riemann surface.Ann. Math. 85 (1967) 303–336

    Article  MathSciNet  Google Scholar 

  20. Seshadri C S, Mumford’s conjecture for GL(2) and applications, in: Proceedings of the Bombay Colloquium on Algebraic geometry (1968) 347–371

  21. Seshadri C S, Moduli of π-vector bundles on an algebraic curve, in: Questions on algebraic varieties, C.I.M.E Varenna 1969, 141–260, Edizioni Gremonese, Roma 1970

    Google Scholar 

  22. Seshadri C S, Quotient spaces modulo reductive algebraic groups.Ann. Math. 95 (1972) 511–556

    Article  MathSciNet  Google Scholar 

  23. Steinberg R, Regular elements of semisimple algebraicgroups.Pub. Math. I.H.E.S. No. 25 (1965) 49–80

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This is the second and concluding part of the thesis of late Professor A Ramanathan; the first part was published in the previous issue.

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Ramanathan, A. Moduli for principal bundles over algebraic curves: II. Proc. Indian Acad. Sci. (Math. Sci.) 106, 421–449 (1996). https://doi.org/10.1007/BF02837697

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