N=2 super Riemann surfaces and algebraic geometry

The geometric framework for N=2 superconformal field theories are described by studying susy2curves - a nickname for N=2 super Riemann surfaces. It is proved that "single" susy2curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems. © 1990 American Institute of Physics.