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

Maxim Kontsevich, Anton Zorich

Research output: Contribution to journalArticlepeer-review

254 Citations (Scopus)

Abstract

Consider the moduli space of pairs (C, ω) where C is a smooth compact complex curve of a given genus and w 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.

Original languageEnglish
Pages (from-to)631-678
Number of pages48
JournalInventiones Mathematicae
Volume153
Issue number3
DOIs
Publication statusPublished - 2003
Externally publishedYes

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