Volumes of Picard modular surfaces

Stover, Matthew

doi:10.1090/S0002-9939-2011-10786-X

Volumes of Picard modular surfaces
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Proc. Amer. Math. Soc. 139 (2011), 3045-3056 Request permission

Abstract:

We show that the conjectural cusped complex hyperbolic 2-orbifolds of minimal volume are the two smallest arithmetic complex hyperbolic 2-orbifolds. We then show that every arithmetic cusped complex hyperbolic 2-manifold of minimal volume covers one of these two orbifolds. We also give all minimal volume manifolds that simultaneously cover both minimal orbifolds.

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