Hodge decomposition for Cousin groups and for Oeljeklaus-Toma manifolds

Otiman, Alexandra; Toma, Matei

doi:10.2422/2036-2145.201812_001

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Hodge decomposition for Cousin groups and for Oeljeklaus-Toma manifolds

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Otiman, Alexandra
Max Planck Institute for Mathematics, Max Planck Society;

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Toma, Matei
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.2422/2036-2145.201812_001
(Publisher version)

https://doi.org/10.48550/arXiv.1811.02541
(Preprint)

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Citation

Otiman, A., & Toma, M. (2021). Hodge decomposition for Cousin groups and for Oeljeklaus-Toma manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 22(2), 485-503. doi:10.2422/2036-2145.201812_001.

Cite as: https://hdl.handle.net/21.11116/0000-0009-4AEA-D

Abstract

We compute the Dolbeault cohomology of geodesically convex domains contained in Cousin groups which satisfy a strong dispersiveness condition. As consequence we obtain a description of the Dolbeault cohomology of Oeljeklaus-Toma manifolds and in particular the fact that the Hodge decomposition holds for their cohomology.