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arXiv · 1905.04212

On subvarieties of singular quotients of bounded domains

Benoît Cadorel·Simone Diverio·Henri Guenancia
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Abstract

Let $X$ be a quotient of a bounded domain in $\mathbb C^n$. Under suitable assumptions, we prove that every subvariety of $X$ not included in the branch locus of the quotient map is of log general type in some orbifold sense. This generalizes a recent result by Boucksom and Diverio, which treated the case of compact, \'etale quotients. Finally, in the case where $X$ is compact, we give a sufficient condition under which there exists a proper analytic subset of $X$ containing all entire curves and all subvarieties not of general type (meant this time in in the usual sense as opposed to the orbifold sense).

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Benoît Cadorel, Simone Diverio, Henri Guenancia. 2019-05-10. On subvarieties of singular quotients of bounded domains. https://doi.org/10.1112/jlms.12660

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