Moduli spaces of SUSY curves and their operads
Enno Ke{\ss}ler, Yuri I. Manin, Yingying Wu

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
