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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 h...

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Publication status:
Published

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume:
357
Issue:
11
Pages:
4329-4347
Publication date:
2005-01-01
DOI:
ISSN:
0002-9947
Source identifiers:
8497
Language:
English
Keywords:
Pubs id:
pubs:8497
UUID:
uuid:3e17b286-5f8e-4462-8066-e7047aa686d8
Local pid:
pubs:8497
Deposit date:
2012-12-19

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