The moduli space of regular stable maps

TL;DR

This paper demonstrates that the moduli space of regular stable maps into a complex manifold can be endowed with a complex orbifold structure using differential geometric methods, specifically Hardy decompositions and Fredholm theory.

Contribution

It introduces a differential geometric approach to establish the orbifold structure of the moduli space, diverging from traditional algebraic geometry techniques.

Findings

Moduli space admits a natural complex orbifold structure.

Differential geometric methods can be effectively used in this context.

Hardy decompositions and Fredholm theory are key tools in the proof.

Abstract

The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy decompositions and Fredholm intersection theory in the loop space of the target manifold.