Genus 4 Supermoduli Space Is Not Projected

The supermoduli stack ${\mathfrak M}_g$, parametrizing smooth unpunctured super Riemann surfaces of genus $g$, is known to be non-projected for $g \ge 5$. We extend this result to the even-spin component of ${\mathfrak M}_4$. This is done by exhibiting an appropriate compact curve in the spin moduli