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’’ susy2 curves 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.

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