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In the lecture, we deal mainly with topological and analytical properties of Riemann surfaces and holomorphic maps between them. Basic concepts we try to explain are covering, homotopic group, divisors, Čech cohomology and the Riemann-Roch theorem.
Last update: Lávička Roman, doc. RNDr., Ph.D. (13.09.2013)
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Basic aspects (algebraic, function theoretic, geometric and topological) of Riemann surfaces. Last update: Somberg Petr, doc. RNDr., Ph.D. (28.10.2019)
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Students should pass an examination.
Last update: Lávička Roman, doc. RNDr., Ph.D. (23.06.2021)
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Bost, J., From Number theory to Physics, Springer, 2010. Forster, O., Lectures on Riemann surfaces, Springer-Verlag, Berlin, 1985. Černý, I., Foundation of analysis in complex domain, Academia, 1997. Narsimhan, R., Compact Riemann surfaces Last update: Krýsl Svatopluk, doc. RNDr., Ph.D. (13.10.2017)
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Lectures based on literature available. Last update: Krýsl Svatopluk, doc. RNDr., Ph.D. (13.10.2017)
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Requirements to the exam correspond to the syllabus to the extent to which topics were covered during the course. Last update: Lávička Roman, doc. RNDr., Ph.D. (23.06.2021)
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Definition and examples of Riemann surfaces.
Holomorphic maps between Riemann surfaces. Meromorphic functions.
Riemann-Hurwitz theorem.
Elliptic functions. The Weierstrass p-function. Jacobi theta functions.
Classification of Riemann surfaces (Uniformization theorem).
Riemann-Roch theorem. Last update: Lávička Roman, doc. RNDr., Ph.D. (13.09.2013)
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Basics on complex variable functions (inclusive definition of Laurent polynomial of a holomorphic function). Last update: Krýsl Svatopluk, doc. RNDr., Ph.D. (13.10.2017)
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