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

2022/06/14 by Etienne Bonnafoux, Bonnafoux, Etienne, Manuel Kany +13
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2206.06595

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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