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

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.

11 pages, 2 figures. Final version based on the referee's report. To appear in Math. Proc. Cambridge Philos. Soc