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Mathematics > Algebraic Geometry

arXiv:1805.00767 (math)
[Submitted on 2 May 2018]

Title:Orbifold K{ä}hler Groups related to arithmetic complex hyperbolic lattices

Authors:Philippe Eyssidieux (IF)
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Abstract: We study fundamental groups of toroidal compactifications of non compact ball quotients and show that the Shafarevich conjecture on holomorphic convexity for these complex projective manifolds is satisfied in dimension 2 provided the corresponding lattice is arithmetic and small enough. The method is to show that the Albanese mapping on an {é}tale covering space generates jets on the interior, if the lattice is small enough. We also explore some specific examples of Picard-Eisenstein type.
Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV); Differential Geometry (math.DG)
Cite as: arXiv:1805.00767 [math.AG]
  (or arXiv:1805.00767v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.00767

Submission history

From: Philippe Eyssidieux [view email] [via CCSD proxy]
[v1] Wed, 2 May 2018 12:34:56 UTC (27 KB)
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