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Real Theta Characteristics And Automorphisms Of A Real Curve

Biswas, Indranil and Gadgil, Siddhartha (2010) Real Theta Characteristics And Automorphisms Of A Real Curve. In: Journal of the Australian Mathematical Society, 88 (1). pp. 29-42.

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Let X be a geometrically irreductble smooth projective cruve defined over R. of genus at least 2. that admits a nontrivial automorphism, sigma. Assume that X does not have any real points. Let tau be the antiholomorphic involution of the complexification lambda(C) of X. We show that if the action of sigma on the set S(X) of all real theta characteristics of X is trivial. then the order of sigma is even, say 2k and the automorphism tau o (sigma) over cap (lambda) of X-C has a fixed point, where (sigma) over cap is the automorphism of X x C-R defined by sigma We then show that there exists X with a real point and admitting a nontrivial automorphism sigma, such that the action of sigma on S(X) is trivial, while X/<sigma > not equal P-R(1) We also give an example of X with no real points and admitting a nontrivial automorphisim sigma such that the automorphism tau o (sigma) over cap (lambda) has a fixed point, the action of sigma on S(X) is trivial, and X/<sigma > not equal P-R(1)

Item Type: Journal Article
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Additional Information: copyright of this article belongs to Australian Mathematical Society.
Keywords: real curve; real theta characteristic; automorphism
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 30 Mar 2010 17:20
Last Modified: 30 Mar 2010 17:20
URI: http://eprints.iisc.ernet.in/id/eprint/26637

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