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A sharp cusp count for complex hyperbolic surfaces and related results


We derive a sharp cusp count for finite volume complex hyperbolic surfaces which admit smooth toroidal compactifications. We use this result, and the techniques developed in Di Cerbo and Di Cerbo (see [5]), to study the geometry of cusped complex hyperbolic surfaces and their compactifications.

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Correspondence to Gabriele Di Cerbo.

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Cerbo, G.D., Di Cerbo, L.F. A sharp cusp count for complex hyperbolic surfaces and related results. Arch. Math. 103, 75–84 (2014).

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Mathematical Subject Classification

  • 32Q45
  • 57M50
  • 14C20


  • Complex hyperbolic surfaces
  • Toroidal compactifications
  • Cusp count