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On the Uniformization of Compact Kähler Orbifolds

Abstract

This article generalizes to Kähler orbifolds the general results on the uniformization of compact Kähler manifolds that were the topic of the author’s communication to the first joint congress of the Vietnamese and French Mathematical Societies held in Huế in August 2012. It is a translation of a French language preprint (Eyssidieux, Sur l’uniformisation des orbifolds Kählériens compacts, 2013).

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Notes

  1. See [13, 14] for topological stacks.

  2. From now on, \(\mathcal{X}\) is compact.

  3. Note that the seminormalization sn:Z snZ is a homeomorphism and that \(sn_{*}O_{Z^{sn}}\) is the subsheaf of the sheaf of continuous functions on Z which are holomorphic on the smooth part of Z.

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Correspondence to Philippe Eyssidieux.

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Eyssidieux, P. On the Uniformization of Compact Kähler Orbifolds. Viet J Math 41, 399–407 (2013). https://doi.org/10.1007/s10013-013-0043-1

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  • DOI: https://doi.org/10.1007/s10013-013-0043-1

Keywords

  • Kähler manifolds
  • Kähler orbifolds
  • Fundamental group
  • Shafarevich conjecture
  • Holomorphic convexity

Mathematics Subject Classification (2000)

  • 32Q30
  • 32J27
  • 32E05