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Harmonic maps and representations of non-uniform lattices of $PU (m, 1)$

Vincent Koziarz; Julien Maubon — 2008

Annales de l’institut Fourier

We study representations of lattices of $PU (m, 1)$ into $PU (n, 1)$ . We show that if a representation is reductive and if $m$ is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic $m$ -space to complex hyperbolic $n$ -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into $PU (n, 1)$ of non-uniform lattices in $PU (1, 1)$ , and more generally of fundamental groups of orientable...

Numerical character of the effectivity of adjoint line bundles

Frédéric Campana; Vincent Koziarz; Mihai Păun — 2012

Annales de l’institut Fourier

In this note we show that, for any log-canonical pair $(X, Δ)$ , $K_{X} + Δ$ is $ℚ$ -effective if its Chern class contains an effective $ℚ$ -divisor. Then, we derive some direct corollaries.

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Harmonic maps and representations of non-uniform lattices of PU ( m , 1 )

Numerical character of the effectivity of adjoint line bundles

Harmonic maps and representations of non-uniform lattices of $PU (m, 1)$