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A note on the theta characteristics of a compact Riemann surface

Published online by Cambridge University Press:  09 April 2009

Indranil Biswas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India e-mail: [email protected]
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Abstract

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Let X be a compact connected Riemann surface and ξ a square root of the holomorphic contangent bundle of X. Sending any line bundle L over X of order two to the image of dim H0(X, ξ ⊗ L) − dim H0(X, ξ) in Z/2Z defines a quadratic form on the space of all order two line bundles. We give a topological interpretation of this quadratic form in terms of index of vector fields on X.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

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