An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves

IIT Madras Course , Prof. T.E. Venkata Balaji

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Lecture 1: The Idea of a Riemann Surface

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        An Introduction to Riemann Surfaces and Algebraic Curves Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit httpwww.nptel.iitm.ac.insyllabus111106044Goals of the LectureTo develop a suitable definition of a structure of a RiemannSurface on a 2-dimensional surface that will allow us to carry outComplex Analysis (i.e., study of holomorphic (or) analytic functions)on the given surface.KeywordsComplex plane, open set, analytic (or) holomorphic function, Cauchy-Riemannequations, complex differentiable, convergent power series, Taylor expansion,Taylor coefficients, open map, biholomorphic map (or) holomorphic isomorphism,homeomorphism (or) topological isomorphism, complex coordinate chart,compatibility of charts, transition functions, Riemann surface structure

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