Decomposition of some Jacobian varieties of dimension 3

Lubjana Beshaj, Tanush Shaska

I-AIMS paper 2013-3 · Published in Artificial Intelligence and Symbolic Computation (AISC 2014), Lecture Notes in Comput. Sci. 8884, Springer · 2014

We discover a family of dimension 3 Jacobian varieties which decompose into three elliptic curves (E, E₁, E₂). Such family does not fall into the well-known cases where such decomposition is induced by the endomorphisms of the Jacobian variety. It is a 2-dimensional subvariety of the hyperelliptic moduli ℋ₃. For any given moduli point 𝔭 ∈ ℋ₃ we determine explicitly if the corresponding genus 3 curve 𝒳 belongs or not to such family. When it does, we can determine explicitly components E, E₁, and E₂ in terms of the absolute invariants t₁, …, t₆ of binary octavics.

MSC classes: Primary 14H10; Secondary 14H37, 14Q05

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