An origami of genus $3$ with arithmetic Kontsevich--Zorich monodromy

TL;DR

This paper constructs a genus 3 origami in the moduli space of translation surfaces with a non-thin Kontsevich--Zorich monodromy, demonstrating a specific arithmetic property using Benoist--Miquel's criterion.

Contribution

It introduces a new example of a genus 3 origami with non-thin monodromy, applying the Benoist--Miquel arithmeticity criterion in this context.

Findings

Constructed an explicit genus 3 origami with specified monodromy properties.

Demonstrated the application of Benoist--Miquel criterion to translation surfaces.

Provided insights into the structure of the moduli space of translation surfaces.

Abstract

In this note, we exploit the arithmeticity criterion of Benoist--Miquel to exhibit an origami in the principal stratum of the moduli space of translation surfaces of genus three whose Kontsevich--Zorich monodromy is not thin in the sense of Sarnak.