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A characterization of complex quasi-projective manifolds uniformized by unit balls

Abstract : In 1988 Simpson extended the Donaldson-Uhlenbeck-Yau theorem to the context of Higgs bundles, and as an application he proved a uniformization theorem which characterizes complex projective manifolds and quasi-projective curves whose universal coverings are complex unit balls. In this paper we give a necessary and su cient condition for quasi-projective manifolds to be uniformized by complex unit balls. This generalizes the uniformization theorem by Simpson. Several byproducts are also obtained in this paper.
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https://hal.archives-ouvertes.fr/hal-02902440
Contributor : Ya Deng <>
Submitted on : Monday, July 26, 2021 - 3:41:07 PM
Last modification on : Thursday, July 29, 2021 - 9:48:30 AM

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  • HAL Id : hal-02902440, version 2
  • ARXIV : 2006.16178

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Ya Deng, Benoit Cadorel. A characterization of complex quasi-projective manifolds uniformized by unit balls. 2021. ⟨hal-02902440v2⟩

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