Superperiods and superstring measure near the boundary of the moduli space of supercurves

2024/08/20 by Giovanni Felder, David Kazhdan, Felder, Giovanni +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2408.11136

openalex publication_date 2024/08/20 · openalex created_date 2024/12/16 · openalex updated_date 2026/07/28

Abstract

We study the behavior of the superperiod map near the boundary of the moduli space of stable supercurves and prove that it is similar to the behavior of periods of classical curves. We consider two applications to the geometry of this moduli space in genus 2, denoted as \mathcal S₂. First, we characterize the canonical projection of \mathcal S₂ in terms of its behavior near the boundary, proving in particular that \mathcal S₂ is not projected. Secondly, we combine the information on superperiods with the explicit calculation of genus 2 Mumford isomorphism, due to Witten, to study the expansion of the superstring measure for genus 2 near the boundary. We also present the proof, due to Deligne, of regularity of the superstring measure on \mathcal S_g for any genus.

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