Weierstrass Prym eigenforms in genus four

Abstract

We prove that for each discriminant $D\equiv 0,1\mathrm{mod}4,D\notin \{4,9\}$, the corresponding Prym eigenform locus discovered by McMullen in the stratum $\mathcal{H}(6)$ is connected. Thus, the projection of any of those loci in the moduli space is a single Teichmüller curve. Along the way, we obtain a classification of primitive square-tiled surfaces in the locus $\mathrm{Prym}(6)$ of Prym forms in $\mathcal{H}(6)$.

37 pages, 9 figures. Comments welcome!