Automorphisms of curves fixing the order two points of the Jacobian

Biswas, Indranil ; Parameswaran, A. J. (2008) Automorphisms of curves fixing the order two points of the Jacobian Geometriae Dedicata, 135 (1). pp. 65-69. ISSN 0046-5755

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Official URL: http://www.springerlink.com/content/q5701l54u76043...

Related URL: http://dx.doi.org/10.1007/s10711-008-9262-0

Abstract

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 σ that fixes pointwise all the order two points of Pic0(X), then we prove that X is hyperelliptic with σ being 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.

Item Type:Article
Source:Copyright of this article belongs to Geometriae Dedicata.
Keywords:Curve: Automorphism: Jacobian: Theta Characteristic
ID Code:35284
Deposited On:04 Jul 2012 13:28
Last Modified:04 Jul 2012 13:28

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