What are some common applications of the Theory of Riemann Surfaces in String Theory?
The main point of Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm.
http://mathworld.wolfram.com/images/eps-gif/RiemannSurface_650.gif
The main point of Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm.
http://mathworld.wolfram.com/images/eps-gif/RiemannSurface_650.gif
