March 4, 2024Open Access

On supercurves of genus 1 with an underlying odd spin structure

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Abstract

We study the standard family of supercurves of genus 1 with an underlying odd spin structures. We give a simple algebraic description of this family and of the compactified family of stable supercurves with one Neveu-Schwarz puncture. We also describe the Gauss-Manin connection on the first de Rham cohomology of this family and compute the superperiods of global differentials.

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Alexander Polishchuk (Mon,) studied this question.

synapsesocial.com/papers/68e75ddfb6db6435876d529c https://doi.org/https://doi.org/10.48550/arxiv.2403.02424

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