On the Nonprojectedness of Supermoduli with Neveu-Schwarz and Ramond Punctures

TL;DR

This paper investigates the structure of supermoduli spaces of Super Riemann Surfaces with various punctures, demonstrating non-projectedness under specific genus and puncture conditions, thus advancing understanding of their geometric properties.

Contribution

It improves previous results by establishing new conditions under which the supermoduli space is not projected, specifically for genus g ≥ n + 5r + 3.

Findings

Supermoduli space is not projected for g ≥ n + 5r + 3.

Refines previous results by Donagi, Witten, and Ott.

Provides conditions linking genus and puncture types to supermoduli space structure.

Abstract

We study the supermoduli space $\mathfrak {M}_{g,n,2r}$ of Super Riemann Surfaces (SRS) of genus $g$, with $n$ Neveu-Schwarz punctures and $2r$ Ramond punctures. We improve the result of Donagi, Witten, and Ott by showing that the supermoduli space $\mathfrak M_{g,n,2r}$ is not projected if $g\geq n+5r+3$.