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On the Jacobian of the Klein Curve

✍ Scribed by Despina T. Prapavessi


Book ID
121526036
Publisher
American Mathematical Society
Year
1994
Tongue
English
Weight
192 KB
Volume
122
Category
Article
ISSN
0002-9939

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Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P 1 , a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curve's jacobian in Weierstrass form and the covering map to its jacobian induced by the K

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Let \(J\) be the Jacobian of the hyperelliptic curve \(Y^{2}=f\left(X^{2}\right)\) over a field \(K\) of characteristic 0 , where \(f\) has odd degree. We shall present an embedding of the group \(J(K) / 2 J(K)\) into the group \(L^{* / L^{* 2}}\) where \(L=K[T] / f(T)\). Since this embedding is der