Inventiones mathematicae

, Volume 153, Issue 3, pp 631–678

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


DOI: 10.1007/s00222-003-0303-x

Cite this article as:
Kontsevich, M. & Zorich, A. Invent. math. (2003) 153: 631. doi:10.1007/s00222-003-0303-x


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.

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  2. 2.Institut Mathématique de RennesUniversité Rennes-1RennesFrance

Personalised recommendations