Global structures for the moduli of (punctured) super riemann surfaces

Abstract

A fine moduli superspace for algebraic super Riemann surfaces with a level- n structure is constructed as a quotient of the split superscheme of local spin-gravitivo fields by an étale equivalence relation. This object is not a superscheme, but still has an interesting structure: it is an algebraic superspace, that is, an analytic superspace with sufficiently many meromorphic functions. The moduli of super Riemann surfaces with punctures (fixed points in the supersurface) is also constructed as an algebraic superspace. Moreover, when one only considers ordinary punctures (fixed points in the underlying ordinary curve), it turns out that the moduli is a true superscheme. We prove furthermore that this moduli superscheme is split.