Generalised Prym Varieties as Fixed Points

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Authors

  • M. S. Narasimhan
     Tata Institute of Fundamental Research, Bombay 400 005 ,IN
  • S. Ramanan
     Tata Institute of Fundamental Research, Bombay 400 005 ,IN

Abstract

Let X be a nonsingular, projective curve of genus g ≥ 2. Then the elements of order r of the Jacobian of X act in a natural way on the moduli space M(r, ξ) of stable vector bundles on X of rank r( ≥ 2) whose determinants are isomorphic to a given line bundle ξ of degree d. We shall assume that r and d are coprime and show that the fixed point variety corresponding to any element μ (strictly) of order r is an abelian variety. In fact, this fixed point variety is isomorphic to the generalised Prym variety (See Remark 3.7) associated to μ.

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Published

1975-12-01

How to Cite

Narasimhan, M. S., & Ramanan, S. (1975). Generalised Prym Varieties as Fixed Points. The Journal of the Indian Mathematical Society, 39(1-4), 1–19. Retrieved from http://www.informaticsjournals.com/index.php/jims/article/view/16633

Issue

Volume 39, Issue 1-4, March-December 1975

Section

Articles

License

Copyright (c) 1975 M. S. Narasimhan, S. Ramanan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

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K. KODAIRA, Characteristic linear systems of complete continuous systems, Amer. J. of Math., 78 (1956), 716-744.

M.S. NARASIMHAN AND S. RAMANAN, Deformations of the moduli space of vector bundles over an algebraic curve. Ann of Math. 101 (1975) 391-417.

S. RAMANAN, The moduli spaces of vector bundles over an algebraic curve, Math. Ann 200, (1973), 69-84.