Connected components of the moduli spaces of Abelian differentials with prescribed singularities
Geometric Topology
2014-04-02 v2 Algebraic Geometry
Abstract
Consider the moduli space of pairs (C,w) 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.
Keywords
Cite
@article{arxiv.math/0201292,
title = {Connected components of the moduli spaces of Abelian differentials with prescribed singularities},
author = {M. Kontsevich and A. Zorich},
journal= {arXiv preprint arXiv:math/0201292},
year = {2014}
}
Comments
42 pages, 12 figures, LaTeX