On the classification of toroidal compactifications with $3\bar{c}_{2}=\bar{c}^{2}_{1}$ and $\bar{c}_{2}=1$

preprint2014arXivOpen access

We classify the smallest finite volume complex hyperbolic surfaces with cusps which admit smooth toroidal compactifications and which are not birational to a bi-elliptic surface. Remarkably, there is only one such surface which appears to be the compactification of a Picard modular surface.

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On the classification of toroidal compactifications with $3\bar{c}_{2}=\bar{c}^{2}_{1}$ and $\bar{c}_{2}=1$

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On the classification of toroidal compactifications with 3cˉ2=cˉ123\bar{c}_{2}=\bar{c}^{2}_{1}3cˉ2​=cˉ12​ and cˉ2=1\bar{c}_{2}=1cˉ2​=1

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On the classification of toroidal compactifications with $3\bar{c}_{2}=\bar{c}^{2}_{1}$ and $\bar{c}_{2}=1$