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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Riemann surfaces SemesterWiSe 2026 / 27 Lecturer Leonard Pille-Schneider Type of course (Veranstaltungsart) Vorlesung German title Riemannsche Flächen Contents Riemann surfaces are 2-dimensional real manifolds endowed a complex structure, for instance the complex plane, 1-dimensional tori (elliptic curves) or the Riemann sphere CP^1. The complex structure allows one to define a notion of holomorphic/meromorphic map between Riemann surfaces, and the tools of function theory and complex analysis can be used to study them. The theory of Riemann surfaces lies at the crossroads between topology, differential geometry, complex analysis and algebraic geometry, and provides a very interesting class of examples for all the mentioned subjects. Topics covered in the lecture will include: elliptic curves, differential forms, algebraic functions and algebraic curves, the Riemann-Roch theorem and Serre duality. Literature R. Miranda, Algebraic Curves and Riemann Surfaces, 1995 S. K. Donaldson, Riemann surfaces, Oxford Graduate Texts in Mathematics, 2011 O. Forster, Lectures on Riemann surfaces, GTM Vol. 81, 1981 Recommended previous knowledge Analysis IV, Funktionentheorie Time/Date Vorlesung Mo & Do 10-12, Übung Mi 10-12 Registration
BAn(2), BV, MV, MArGeo, MGAGeo ECTS 9 |