Geodesic
Moduli space of meromorphic differentials with marked horizontal separatrices
Boissy, Corentin1
1CNRS, Institut Mathématique de Toulouse, Université de Toulouse, UMR5219, Toulouse, France
Algebraic and Geometric Topology, Tome 20 (2020) no. 5, pp. 2373-2412
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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 g > 0, there are at most two such components, except in the hyperelliptic case.

DOI : 10.2140/agt.2020.20.2373
Classification : 32G15, 30F30, 57R15
Keywords: meromorphic differentials, translation surfaces, moduli spaces

Boissy, Corentin  1

1 CNRS, Institut Mathématique de Toulouse, Université de Toulouse, UMR5219, Toulouse, France 
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Boissy, Corentin. Moduli space of meromorphic differentials with marked horizontal separatrices. Algebraic and Geometric Topology, Tome 20 (2020) no. 5, pp. 2373-2412. doi: 10.2140/agt.2020.20.2373

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