Abstract
Every complex algebraic curve is a two-dimensional oriented surface. As we already know, the topology of such surfaces is very simple: for a compact surface, the topology is uniquely determined by its genus (or, equivalently, its Euler characteristic). However, along with a topological structure, a curve has a complex structure. It singles out analytic functions among all the functions on the curve.
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Sometimes, in the definition of a local coordinate, one requires that the point A is mapped to the center of the disk.
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Kazaryan, M.E., Lando, S.K., Prasolov, V.V. (2018). Complex Structure and the Topology of Curves. In: Algebraic Curves. Moscow Lectures, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-030-02943-2_3
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DOI: https://doi.org/10.1007/978-3-030-02943-2_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-02942-5
Online ISBN: 978-3-030-02943-2
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