Skip to main content

Geometry of Moduli Spaces (The work of C.S.Seshadri)

  • Chapter
A Tribute to C. S. Seshadri
  • 184 Accesses

Abstract

The aim of this brief article is to survey three fundamental papers of C.S.Seshadri on the moduli space of semi-stable bundles and their desingularisation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 68.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. M. Atiyah and R. Bott: Yang-Mills Equations over Riemann Surfaces, Proc. Trans.R.Soc.Lond., A 308, (1982), 523–615.

    Article  MathSciNet  MATH  Google Scholar 

  2. V. Balaji: Intermediate Jacobian of some moduli spaces of vector bundles on curves, American Jour Math, 112, (1990), 611–630.

    Article  MathSciNet  MATH  Google Scholar 

  3. V. Balaji and C.S. Seshadri: Cohomology of a moduli space of vector bundles, The Grothendieck Festchrift Volume 1, Birhhauser, (1990) pp. 87–120.

    Google Scholar 

  4. V. Balaji and C.S. Seshadri: Cohomology of a moduli space of vector bundles, The Grothendieck Festchrift Volume 1, Birhhauser, (1990) pp. 87–120.

    Google Scholar 

  5. V. Balaji and P.A. Vishwanath: Deformations of certain moduli spaces of vector bundles, Amer. Jour. Math., Vol. 115, No. 2 (1993) 279–303.

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Balaji, I. Biswas and D.S. Nagaraj: Principal bundles over projective manifolds with parabolic structure over a divisor. Tôhoku Math. Jour. 53 (2001), 337–368.

    Article  MathSciNet  MATH  Google Scholar 

  7. V. Balaji and C.S. Seshadri: Semistable Principal Bundles-I (in characteristic zero), Journal of Algebra., 258, 321–347.

    Google Scholar 

  8. V. Balaji and A.J. Parameswaran: Semistable principal bundles-II (in positive characteristics). (to appear in Transformation Groups)

    Google Scholar 

  9. G. Faltings: Stable G-bundles and projective connections, J. Alg. Geom. 2 (1993), 507–568.

    MathSciNet  MATH  Google Scholar 

  10. D. Mumford, J. Fogarty and F. Kirwan: Geometric Invariant theory, Ergebnisse 34, Springer 3rd Edition.

    Google Scholar 

  11. M.S. Narasimhan and C.S. Seshadri: Holomorphic vector bundles on a compact Riemann surface, Math.Annalen, 155, (1964), 69–80.

    Article  MathSciNet  MATH  Google Scholar 

  12. M.S. Narasimhan and C.S. Seshadri: Stable and unitary vector bundles on a compact Riemann surface, Annals of Mathematics, 82, (1965) pp 540–567.

    Article  MathSciNet  MATH  Google Scholar 

  13. M.S. Narasimhan and S. Ramanan: Moduli of vector bundles on a compact Riemann surface, Annals of Mathematics, 89, (1969), 14–51.

    Article  MathSciNet  MATH  Google Scholar 

  14. M.S. Narasimhan and S. Ramanan: Geometry of Hecke Cycles-I, C.P.Ramanujam — A Tribute, (Bombay TIFR), (1978).

    Google Scholar 

  15. N. Nitsure, Moduli spaces of semistable pairs on a curve, Proc.London Math Soc, 62, (1991), 275–300.

    Article  MathSciNet  MATH  Google Scholar 

  16. M. V. Nori: The fundamental group scheme, Proc.Ind.Acad.Sci (Math.Sci) 91 (1982), 73–122.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. Ramanathan: Stable principal bundles on a compact Riemann surface — Construction of moduli space (Thesis, Bombay University 1976).

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  19. C.S. Seshadri: Spce of unitary bundles on a compact Riemann surface, Annals of Mathematics, 85, (1967), 303–336.

    Article  MathSciNet  MATH  Google Scholar 

  20. C.S. Seshadri : Mumford’s Conjecture for GL(2) and applications, Algebraic Geometry, Bombay Colloquium (1968), 347–371.

    Google Scholar 

  21. C.S. Seshadri: Fibrés vectoriels sur un courbes algébriques, Asterisque 96 (1982).

    Google Scholar 

  22. C.S. Seshadri: Desingularisation of moduli varieties of vector bundles on curves, International Symp. on Algebraic geometry, (ed.) M. Nagata (Kyoto), (1977), 155–184.

    Google Scholar 

  23. C. Simpson: Higgs bundles and Local systems, Pub. I.H.E.S. 75 (1992), 5–95.

    Article  MathSciNet  MATH  Google Scholar 

  24. C. Simpson: Moduli of representations of the fundamental group of a smooth projective variety-I, Pub. I.H.E.S. 79 (1994) pp 47–129.

    Article  MathSciNet  MATH  Google Scholar 

  25. C. Simpson: Moduli of representations of the fundamental group of a smooth projective variety-II, Pub. I.H.E.S. 80 (1995), 5–79.

    Article  MATH  Google Scholar 

  26. T.E. Venkata Balaji, Limits of rank 4 Azumaya algebras and applications to desingularisation Proc Ind.Acad.Sci 112 (2002), 485–537.

    MATH  Google Scholar 

  27. E. Vieweg, Quasi-Projective Moduli of Polarised Manifolds, Ergebnisse Vol 30, Springer Verlag, (1995)

    Book  Google Scholar 

  28. Lieven Le Bruyn and Z. Reichstein, Smoothness in algebraic geography. Proc. London Math. Soc. (3) 79 (1999), no. 1, 158–190.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

V. Lakshmibai V. Balaji V. B. Mehta K. R. Nagarajan K. Pranjape P. Sankaran R. Sridharan

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Hindustan Book Agency

About this chapter

Cite this chapter

Balaji, V. (2003). Geometry of Moduli Spaces (The work of C.S.Seshadri). In: Lakshmibai, V., et al. A Tribute to C. S. Seshadri. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-11-8_2

Download citation

Publish with us

Policies and ethics