N=2 supertori and their representation as algebraic curves

Abstract

N=2 supertori (N=2 super-Riemann surfaces of genus 1) are classified according to their superconformal equivalence classes. A detailed description of the corresponding supermoduli space is based on this classification. Superelliptic functions are constructed and used for representing the supertori as algebraic varieties in projective superspace. The boundary of N=2, genus 1 supermoduli space is discussed.