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Moduli space of
meromorphic differentials with marked horizontal
separatrices
Corentin Boissy |
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Algebraic & Geometric Topology 20 (2020) 2373–2412
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Abstract |
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We study framed translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces, for which a horizontal separatrix is marked for each pole or zero. Such geometric structures naturally appear when studying flat geometry surfaces “near” the Deligne–Mumford boundary. We compute the number of connected components of the corresponding strata, and give a simple topological invariant that distinguishes them. In particular we see that for , there are at most two such components, except in the hyperelliptic case. |
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Keywords
meromorphic differentials, translation surfaces, moduli
spaces
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Mathematical Subject Classification 2010
Primary: 32G15
Secondary: 30F30, 57R15
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References |
Publication
Received: 6 April 2018
Revised: 5 April 2019
Accepted: 1 December 2019
Published: 4 November 2020
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Authors |
| Corentin Boissy | |
| CNRS, Institut Mathématique de
Toulouse Université de Toulouse UMR5219 Toulouse France |
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