Automorphisms of curves fixing the order two points of the Jacobian

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Let X be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic different from two. If X admits a nontrivial automorphism σthat fixes pointwise all the order two points of Pic}^0(X), then we prove that X is hyperelliptic with σbeing the unique hyperelliptic involution. As a corollary, if a nontrivial automorphisms σ' of X fixes pointwise all the theta characteristics on X, then X is hyperelliptic with σ' being its hyperelliptic involution.

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Algebraic Geometry, 14H37, 14H40

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http://salesiana.dossiersoluciones.com/handle/123456789/158478

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.1599
 http://arxiv.org/abs/0804.1599

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arXiv