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 http://www.nptel.iitm.ac.in/syllabus/111106044/
Goals 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
surfaces
Keywords:
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