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2020 Moduli space of meromorphic differentials with marked horizontal separatrices
Corentin Boissy
Algebr. Geom. Topol. 20(5): 2373-2412 (2020). 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.

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Corentin Boissy. "Moduli space of meromorphic differentials with marked horizontal separatrices." Algebr. Geom. Topol. 20 (5) 2373 - 2412, 2020. https://doi.org/10.2140/agt.2020.20.2373

Information

Received: 6 April 2018; Revised: 5 April 2019; Accepted: 1 December 2019; Published: 2020
First available in Project Euclid: 10 November 2020

MathSciNet: MR4171569
Digital Object Identifier: 10.2140/agt.2020.20.2373

Subjects:
Primary: 32G15
Secondary: 30F30, 57R15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 5 • 2020
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