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arXiv · 2206.06595

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

Etienne Bonnafoux·Manuel Kany·Pascal Kattler·Carlos Matheus·Rogelio Niño·Manuel Sedano-Mendoza·Ferrán Valdez·Gabriela Weitze-Schmithüsen
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Abstract

The variations of Hodge structures of weight one associated to square-tiled surfaces naturally generate interesting subgroups of integral symplectic matrices called Kontsevich--Zorich monodromies. In this paper, we show that arithmetic groups are frequent among the Kontsevich--Zorich monodromies of square-tiled surfaces of low genera $g$.

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Etienne Bonnafoux, Manuel Kany, Pascal Kattler, Carlos Matheus, Rogelio Niño, Manuel Sedano-Mendoza, Ferrán Valdez, Gabriela Weitze-Schmithüsen. 2022-06-14. Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces. https://arxiv.org/abs/2206.06595

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