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Translation surfaces and periods of meromorphic differentials

Chenakkod, S and Faraco, G and Gupta, S (2022) Translation surfaces and periods of meromorphic differentials. In: Proceedings of the London Mathematical Society .

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Official URL: https://doi.org/10.1112/plms.12432


Let (Formula presented.) be an oriented surface of genus (Formula presented.) and (Formula presented.) punctures. The periods of any meromorphic differential on (Formula presented.), with respect to a choice of complex structure, determine a representation (Formula presented.) where (Formula presented.) is the first homology group of (Formula presented.). We characterise the representations that thus arise, that is, lie in the image of the period map (Formula presented.). This generalises a classical result of Haupt in the holomorphic case. Moreover, we determine the image of this period map when restricted to any stratum of meromorphic differentials, having prescribed orders of zeros and poles. Our proofs are geometric, as they aim to construct a translation structure on (Formula presented.) with the prescribed holonomy (Formula presented.). Along the way, we describe a connection with the Hurwitz problem concerning the existence of branched covers with prescribed branching data. © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

Item Type: Journal Article
Publication: Proceedings of the London Mathematical Society
Publisher: John Wiley and Sons Ltd
Additional Information: The copyright for this article belongs to John Wiley and Sons Ltd
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 18 Mar 2022 11:57
Last Modified: 18 Mar 2022 11:57
URI: http://eprints.iisc.ac.in/id/eprint/71594

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