Moduli space of meromorphic differentials with marked horizontal separatrices

Corentin Boissy (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Topologie géométrique [math.GT]

Corentin Boissy. Moduli space of meromorphic differentials with marked horizontal separatrices. Algebraic & Geometric Topology, 2020, 20, pp.2373-2412. ⟨10.2140/agt.2020.20.2373⟩. ⟨hal-01170878v5⟩