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

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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.

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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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Authors and Affiliations

  1. Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80.010, 3508 TA , Utrecht, The Netherlands

    Eduard Looijenga

  2. Dipartimento di Matematica “Guido Castelnuovo”, “Sapienza” Università di Roma, Piazzale Aldo Moro 5, 00185 , Rome, Italy

    Gabriele Mondello

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  1. Eduard Looijenga
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  2. Gabriele Mondello
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Correspondence to Gabriele Mondello.

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Looijenga, E., Mondello, G. The fine structure of the moduli space of abelian differentials in genus 3. Geom Dedicata 169, 109–128 (2014). https://doi.org/10.1007/s10711-013-9845-2

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  • DOI: https://doi.org/10.1007/s10711-013-9845-2

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