Explicit Constructions for Genus 3 Jacobians
classification
🧮 math.AG
keywords
explicitgenusopenaffinealgorithmscanonicalconstructconstruction
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Given a canonical genus three curve $X=\{F=0\}$, we construct, emulating Mumford discussion for hyperelliptic curves, a set of equations for an affine open subset of the jacobian $JX$. We give explicit algorithms describing the law group in $JX$. Finally we introduce a related construction by means of an imbedding of the open set previously described in a Grassmanian variety.
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