Classification and arithmeticity of toroidal compactifications with 3c2 = c12 = 3

Di Cerbo, Luca¹ ; Stover, Matthew²

¹ Mathematics Section, International Centre for Theoretical Physics, Trieste, Italy
² Department of Mathematics, Temple University, Philadelphia, PA, United States

Geometry & topology, Tome 22 (2018) no. 4, pp. 2465-2510.

Résumé

We classify the minimum-volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications, and we explicitly construct their compactifications. There are five such surfaces, and they are all arithmetic; ie they are associated with quotients of the ball by an arithmetic lattice. Moreover, the associated lattices are all commensurable. The first compactification, originally discovered by Hirzebruch, is the blowup of an abelian surface at one point. The others are bielliptic surfaces blown up at one point. The bielliptic examples are new and are the first known examples of smooth toroidal compactifications birational to bielliptic surfaces.

Détail

DOI : 10.2140/gt.2018.22.2465

Classification : 22E40, 20H10, 57M50, 14M27, 32Q45, 11F60
Keywords: toroidal compactifications, complex hyperbolic manifolds, minimal volume manifolds, arithmetic lattices

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