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 9: A First Classification of Riemann Surfaces

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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 Lecture - To get an idea of the classification of Riemann surfaces that can be arrived at based on the fundamental group, using the theory of covering spaces- To get introduced to the notions of moduli problem, moduli space, number of moduli, fine and coarse classification, and to write these down for simple Riemann surfacesKeywords Biholomorphic map or isomorphism of Riemann surfaces, classification of Riemann surfaces, universal covering of a Riemann surface, abelian fundamental group, complex plane, unit disc, upper half-plane, punctured plane, punctured unit disc, cylinder, complex torus, annulus, Riemann sphere, g-torus, coarse classification, fine classification, moduli problem, moduli theory, moduli space, number of moduli

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