Abstract
We give three examples of non-hyperelliptic curves of genus 4 whose Jacobian varieties are isomorphic to products of four elliptic curves. Two of the examples belong to one-parameter families of curves whose Jacobian varieties are isomorphic to products of two 2-dimensional complex tori. By constructing analogous families, we prove that for each $n>1$, there is a one-parameter family of non-hyperelliptic curves of genus $2n$ whose Jacobian varieties are isomorphic to products of two $n$-dimensional tori.
Citation
Ryo Nakajima. "On splitting of certain Jacobian varieties." J. Math. Kyoto Univ. 47 (2) 391 - 415, 2007. https://doi.org/10.1215/kjm/1250281052
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