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Geometriae Dedicata

, Volume 169, Issue 1, pp 109–128 | Cite as

The fine structure of the moduli space of abelian differentials in genus 3

  • Eduard Looijenga
  • Gabriele Mondello
Original paper

Abstract

The moduli space of curves endowed with a nonzero abelian differential admits a natural stratification according to the configuration of its zeroes. We give a description of these strata for genus 3 in terms of root system data. For each non-open stratum we obtain a presentation of its orbifold fundamental group.

Keywords

Abelian differentials Translation surfaces Moduli space of curves  Root systems Artin groups 

Mathematics Subject Classification (2000)

14H45 32G15 

Notes

Acknowledgments

E.L. wishes to thank the Mathematical Sciences Research Institute and the Tsinghua Mathematics Department for support and hospitality during the period part of this work was done. G.M. would like to thank Enrico Arbarello for frequent and useful exchange of ideas about spaces of abelian differentials and the Park City Mathematical Institute for hospitality in July 2011.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands
  2. 2.Dipartimento di Matematica “Guido Castelnuovo”“Sapienza” Università di RomaRomeItaly

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