Moduli space of meromorphic differentials with marked horizontal separatrices

Corentin Boissy

doi:10.2140/agt.2020.20.2373

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arXiv · 1507.00555

Moduli space of meromorphic differentials with marked horizontal separatrices

Corentin Boissy

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Abstract

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.

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BibTeX RIS

Corentin Boissy. 2015-07-02. Moduli space of meromorphic differentials with marked horizontal separatrices. https://doi.org/10.2140/agt.2020.20.2373

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