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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