Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications

Di Cerbo, Luca; Stover, Matthew

doi:10.1090/tran/7650

Punctured spheres in complex hyperbolic surfaces and bielliptic ball quotient compactifications
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by Luca F. Di Cerbo and Matthew Stover PDF

Trans. Amer. Math. Soc. 372 (2019), 4627-4646 Request permission

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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