Generalised Prym Varieties as Fixed Points
Authors
-
Tata Institute of Fundamental Research, Bombay 400 005 ,IN
M. S. Narasimhan -
Tata Institute of Fundamental Research, Bombay 400 005 ,INS. Ramanan
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.Downloads
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Copyright (c) 1975 M. S. Narasimhan, S. Ramanan
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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