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Two-dimensional families of hyperelliptic Jacobians with big monodromy
Let $K$ be a global field of characteristic different from $2$ and $u(x)\in K[x]$ be an irreducible polynomial of even degree $2g\ge 6$ whose Galois group over $K$ is either the full symmetric group $\mathbf {S}_{2g}$ or the alternating group $\mathbf {A}_{2g}$. We describe explicitly how to choose (infinitely many) …