On the classification of toroidal compactifications with 3c₂=c²₁ and c₂=1

2013/09/21 by Di Cerbo, Luca Fabrizio
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1309.5516

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.

Related

• A sharp cusp count for complex hyperbolic surfaces and related results
• Finite volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications
• Toroidal compactifications of torsion free local complex hyperbolic spaces
• Volumes of Picard modular surfaces
• Multiple realizations of varieties as ball quotient compactifications