Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications

Luca F. Di Cerbo; Matthew Stover

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arXiv · 1801.01575

Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications

Luca F. Di Cerbo·Matthew Stover

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Abstract

In this paper, we study punctured spheres in two dimensional ball quotient compactifications $(X, D)$. For example, we show that smooth toroidal compactifications of ball quotients cannot contain properly holomorphically embedded $3$-punctured spheres. We also use totally geodesic punctured spheres to prove ampleness of $K_X + \alpha D$ for $\alpha \in (\frac{1}{4}, 1)$, giving a sharp version of a theorem of the first author with G. Di Cerbo. Finally, we produce the first examples of bielliptic ball quotient compactifications modeled on the Gaussian integers.

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BibTeX RIS

Luca F. Di Cerbo, Matthew Stover. 2018-01-04. Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications. https://arxiv.org/abs/1801.01575

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