Moduli space of meromorphic differentials with marked horizontal separatrices

Boissy, Corentin

doi:10.2140/agt.2020.20.2373

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Moduli space of meromorphic differentials with marked horizontal separatrices

Corentin Boissy

Algebraic & Geometric Topology 20 (2020) 2373–2412

DOI: 10.2140/agt.2020.20.2373

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.

Keywords

meromorphic differentials, translation surfaces, moduli spaces

Mathematical Subject Classification 2010

Primary: 32G15

Secondary: 30F30, 57R15

References

Publication

Received: 6 April 2018

Revised: 5 April 2019

Accepted: 1 December 2019

Published: 4 November 2020

Authors

Corentin Boissy
CNRS, Institut Mathématique de Toulouse Université de Toulouse UMR5219 Toulouse France

Volume 20, issue 5 (2020)