Arithmeticity of the Kontsevich–Zorich monodromies of certain families of origamis

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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 g .