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We give an explicit construction of a family of lattices in PU (1, 2) originally constructed by Livné. Following Thurston, we construct these lattices as the modular group of certain Euclidean cone metrics on the sphere. We give connections between these groups and other groups of complex hyperbolic isometries.

Let$Z$be the zero set of a holomorphic section$f$of a Hermitian vector bundle. It is proved that the current of integration over the irreducible components of$Z$of top degree, counted with multiplicities, is a product of a residue factor$R$^{$f$}and a “Jacobian factor”. There is also a relation to the Monge-Ampère expressions ($dd$^{$c$}log|$f$|)^{$k$}, which we define for all positive powers$k$.

The problem of$subextension$of plurisubharmonic functions is considered. Recently it was shown by Cegrell–Zeriahi, that subextension is always possible for negative plurisubharmonic functions in the energy class ℱ. In this paper we construct, for every hyperconvex domain Ω, a negative plurisubharmonic function in the class ℰ which cannot be subextended. Given any pseudoconvex domain we construct a pluriharmonic function that cannot be subextended.