\begin{document}
\title{On holomorphic actions of higher rank lattices on Kaehler manifolds}
\author{A. Zeghib}
Let $M$ be a compact Kaehler manifold of dimension $n$,
and $\Gamma$ a lattice of $SL(m, {\bf R})$ acting holomorphically and
non-trivially (i.e. the action does not factorize through an action of
a finite group). Similarly to the case of linear representations, S. Cantat (following
an argument by Dinh and Sibony) proved that $m \leq n+1$, with equality exactly in the case of the projective action of $SL(n+1, {\bf R})$
on ${\bf C}P^n$. Such a non-linear rigidity result can be considered as answering a
variant of a question by R. Zimmer. We are dealing here with the characterization of the case $m= n$, where one knows the usual affine
action of finite index subgroups of $SL(n, {\bf Z})$ on the torus.
\end{document}