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Connected components of the moduli spaces of Abelian differentials with prescribed singularities

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Consider the moduli space of pairs (C,ω) where C is a smooth compact complex curve of a given genus and ω is a holomorphic 1-form on C with a given list of multiplicities of zeroes. We describe connected components of this space. This classification is important in the study of dynamics of interval exchange transformations and billiards in rational polygons, and in the study of geometry of translation surfaces.

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Authors and Affiliations

  1. Institut des Hautes Études Scientifiques, Le Bois-Marie, 35 Route de Chartres, F-91440, Bures-sur-Yvette, France

    Maxim Kontsevich

  2. Institut Mathématique de Rennes, Université Rennes-1, Campus de Beaulieu, 35042, Rennes, France

    Anton Zorich

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  1. Maxim Kontsevich
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  2. Anton Zorich
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Correspondence to Maxim Kontsevich or Anton Zorich.

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Kontsevich, M., Zorich, A. Connected components of the moduli spaces of Abelian differentials with prescribed singularities. Invent. math. 153, 631–678 (2003). https://doi.org/10.1007/s00222-003-0303-x

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  • DOI: https://doi.org/10.1007/s00222-003-0303-x

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