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

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 $g\ge n+5r+3$.