On the non-Transversality of the Hyperelliptic Locus and the Supersingular Locus for $g=3$

This paper gives a criterion for a moduli point to be a point of non-transversal intersection of the hyperelliptic locus and the supersingular locus in the Siegel moduli stack ${\mathfrak{A}}_3\times {\mathbb{F}}_p$. It is shown that for infinitely many primes $p$ there exists such a point.