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The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field. (English) Zbl 0723.14023

Summary: An embedding of the Jacobian variety of a curve \({\mathcal C}\) of genus 2 is given, together with an explicit set of defining equations. A pair of local parameters is chosen, for which the induced formal group is defined over the same ring as the coefficients of \({\mathcal C}\). It is not assumed that \({\mathcal C}\) has a rational Weierstrass point, and the theory presented applies over an arbitrary ground field (of characteristic \(\neq 2, 3\), or 5).

MSC:

14H40 Jacobians, Prym varieties
14L05 Formal groups, \(p\)-divisible groups
14Q05 Computational aspects of algebraic curves
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References:

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