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TEICHMÜLLER CURVES IN HYPERELLIPTIC COMPONENTS OF MEROMORPHIC STRATA

Part of: Deformations of analytic structures

Published online by Cambridge University Press:  26 March 2025

Martin Möller Open the ORCID record for Martin Möller [Opens in a new window] ,
Scott Mullane ,
Benjamin Bakker  and
Scott Mullane
Martin Möller*
Affiliation:
Institut für Mathematik, Goethe-Universität Frankfurt, Robert-Mayer-Str. 6-8, 60325 Frankfurt am Main, Germany
Scott Mullane
Affiliation:
School of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia ([email protected])
Benjamin Bakker
Affiliation:
Dept. of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA ([email protected])
Scott Mullane
Affiliation:
School of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia ([email protected])
*
([email protected])
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Abstract

We provide a complete classification of Teichmüller curves occurring in hyperelliptic components of the meromorphic strata of differentials. Using a non-existence criterion based on how Teichmüller curves intersect the boundary of the moduli space we derive a contradiction to the algebraicity of any candidate outside of Hurwitz covers of strata with projective dimension one, and Hurwitz covers of zero residue loci in strata with projective dimension two.

Keywords

Teichmüller curvesstrata of meromorphic differentialslinear manifolds

MSC classification

Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , First View , pp. 1 - 26
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

Research of M.M is supported by the DFG-project MO 1884/2-1 and the Collaborative Research Centre TRR 326 “Geometry and Arithmetic of Uniformized Structures”.

Research of S.M is supported by the Alexander von Humboldt Foundation, ERC Advanced Grant “SYZYGY”, and DECRA Grant DE220100918 from the Australian Research Council

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