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A surface is a two-dimensional topological manifold. The term can also be used to describe a smooth surface, depending on the context.

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Abel-Jacobi map for regular fibered surfaces.

Let $f:C\to S$ be a regular fibered surface where $S=Spec(R)$, $R=dvr$. Assume $C$ has smooth geometrically integral generic fibre $C_K$. We also assume the existence of a section $x\in C(S)$. Let $ …
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