Translation surfaces with large systoles

In this paper, we continue to investigate the systolic landscape of translation surfaces started in [T. Columbus, F. Herrlich, B. Muetzel and G. Weitze-Schmithüsen, Systolic geometry of translation surfaces, Exp. Math. (2022), doi:10.1080/10586458.2022.2108946]. We show that there exists an infinite sequence of surfaces (Sgk)k of genus gk, where gk →∞ with large systoles. On the other hand, we show that for the hyperelliptic translation surfaces one can always find homology bases where a large number of loops in the basis are short.