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Towers of 2-covers of hyperelliptic curves

Abstract:

In this article, we give a way of constructing an unramified Galois cover of a hyperelliptic curve. The geometric Galois-group is an elementary abelian 2-group. The construction does not make use of the embedding of the curve in its Jacobian and it readily displays all subcovers. We show that the cover we construct is isomorphic to the pullback along the multiplication-by-2 map of an embedding of the curve in its Jacobian. We show that the constructed cover has an abundance of elliptic and hy...

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Publication date:
2005-01-01
URN:
uuid:50465a30-7f8d-499a-9425-9960e7f868bd
Local pid:
oai:eprints.maths.ox.ac.uk:250

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