Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces II

TL;DR

This paper proves the arithmeticity of Kontsevich--Zorich monodromies for specific infinite families of square-tiled surfaces across genera four to six, extending previous work in the field.

Contribution

It extends prior research by establishing the arithmeticity of monodromies for new families of square-tiled surfaces in higher genera.

Findings

Arithmeticity of monodromies confirmed for genus four, five, and six surfaces.

Extends the scope of previous work on Kontsevich--Zorich monodromies.

Provides new insights into the structure of square-tiled surfaces.

Abstract

In this note, we extend the scope of our previous work joint with Bonnafoux, Kattler, Ni\~no, Sedano-Mendoza, Valdez and Weitze-Schmith\"usen by showing the arithmeticity of the Kontsevich--Zorich monodromies of infinite families of square-tiled surfaces of genera four, five and six.