On the classification of toroidal compactifications with $3{\bar{c}}_2={\bar{c}}_1^2$ and ${\bar{c}}_2=1$

Abstract

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.

The argument in the bi-elliptic case has to be extended and it is in progress. Typos corrected and references updated

References in corpus (1)

• Effective results for complex hyperbolic manifolds