# The Kodaira dimension of complex hyperbolic manifolds with cusps

@article{Bakker2017TheKD, title={The Kodaira dimension of complex hyperbolic manifolds with cusps}, author={Benjamin Bakker and Jacob Tsimerman}, journal={Compositio Mathematica}, year={2017}, volume={154}, pages={549 - 564} }

We prove a bound relating the volume of a curve near a cusp in a complex ball quotient $X=\mathbb{B}/\unicode[STIX]{x1D6E4}$ to its multiplicity at the cusp. There are a number of consequences: we show that for an $n$ -dimensional toroidal compactification $\overline{X}$ with boundary $D$ , $K_{\overline{X}}+(1-\unicode[STIX]{x1D706})D$ is ample for $\unicode[STIX]{x1D706}\in (0,(n+1)/2\unicode[STIX]{x1D70B})$ , and in particular that $K_{\overline{X}}$ is ample for $n\geqslant 6$ . By an…

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