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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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Two elliptic curves not dominated by a genus two curve

Let $k$ be a number field and let $E$ and $E'$ be elliptic curve over $k$. There is a genus two curve $X$ over $\overline{k}$ which dominates $E$ and $E'$. Question. Is there a genus two curve $X$ o …
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