Analytic and Algebraic Deformations of Super Riemann Surfaces

TL;DR

This paper explores the relationship between analytic and algebraic deformations of super Riemann surfaces, showing an analogous correspondence to that in complex manifolds, with implications for understanding their complex structures.

Contribution

It establishes an analogous correspondence between analytic and algebraic deformations for super Riemann surfaces, extending known results from complex manifolds.

Findings

Analytic and algebraic deformations of super Riemann surfaces are infinitesimally related.

The correspondence between these deformations mirrors that of complex manifolds.

Provides a framework for understanding complex structure perturbations in supergeometry.

Abstract

By analytic deformations of complex structures, we mean perturbations of the Dolbeault operator. By algebraic deformations of complex structures, we mean deformations of holomorphic glueing data. For complex manifolds there is, infinitesimally, a correspondence between these two types deformations. In this article we argue that an analogous correspondence holds between the analytic and algebraic deformations of a super Riemann surface.