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        The Riemann-Hurwitz formula

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        The Riemann Hurwitz formula final (1).pdf (1.445Mb)
        Publication date
        2021
        Author
        Bosch, S.
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        Summary
        In this thesis we discuss Riemann surfaces and (possibly ramified) coverings. We then discuss and prove the Riemann-Hurwitz formula. One of the applications of the Riemann-Hurwitz formula is that it can be used to prove Hurwitz's automorphisms theorem. We discuss this theorem and subsequently prove it. This thesis is ended by giving a short discussion on the equivalence of categories of compact Riemann surfaces and irreducible, non-singular algebraic curves over the complex plane.
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        https://studenttheses.uu.nl/handle/20.500.12932/1166
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