Biswas, Indranil ; Gadgil, Siddhartha
(2010)
*Real theta characteristics and automorphisms of a real curve*
Journal of the Australian Mathematical Society, 88
(1).
pp. 29-42.
ISSN 1446-7887

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Official URL: http://journals.cambridge.org/abstract_S1446788709...

Related URL: http://dx.doi.org/10.1017/S1446788709000305

## Abstract

Let X be a geometrically irreductble smooth projective cruve defined over R. of genus at least 2. that admits a nontrivial automorphism, σ. Assume that X does not have any real points. Let τ be the antiholomorphic involution of the complexification λ(C) of X. We show that if the action of σ 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 τ o (σ) over cap (λ) of X-C has a fixed point, where (σ) 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 σ on S(X) is trivial, while X/σ ≠ P-R(1) We also give an example of X with no real points and admitting a nontrivial automorphisim sigma such that the automorphism τ o (σ) over cap (λ) has a fixed point, the action of sigma on S(X) is trivial, and X/σ ≠ P-R(1).

Item Type: | Article |
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Source: | Copyright of this article belongs to Australian Mathematical Society. |

Keywords: | Real curve; Real theta characteristic; Automorphism |

ID Code: | 3535 |

Deposited On: | 12 Oct 2010 04:18 |

Last Modified: | 12 Oct 2010 04:18 |

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