Real Theta Characteristics and Automorphisms of a Real Curve
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چکیده
Let X be a geometrically irreducible smooth projective curve, defined over R, of genus at least two that admits nontrivial automorphisms. Fix a nontrivial automorphism σ of X. Assume that X does not have any real points. Then σ acts trivially on the set of all real theta characteristics of X if and only if X is hyperelliptic with σ being the unique hyperelliptic involution of X. Examples are given showing that the condition that X does not have any real points is necessary.
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تاریخ انتشار 2007