Moduli spaces of SUSY curves and their operads

TL;DR

This paper extends the operad framework of moduli spaces to include SUSY curves, integrating supergeometric structures with combinatorial graph methods to develop a SUSY operad with applications in supergeometry.

Contribution

It introduces a novel SUSY operad framework for moduli spaces of SUSY curves, incorporating supergeometric structures and dual graph constructions.

Findings

Construction of the SUSY operad with Neveu-Schwarz and Ramond punctures

Description of the combinatorics of SUSY curve graphs

Extension of moduli space operads to supergeometric contexts

Abstract

This article generalizes the operad of moduli spaces of curves to SUSY curves. SUSY curves are algebraic curves with additional supersymmetric or supergeometric structure. Here, we focus on the description of the relevant category of graphs and its combinatorics as well as the construction of dual graphs of SUSY curves and the SUSY operad taking values in a category of moduli spaces of SUSY curves with Neveu-Schwarz and Ramond punctures.