The Toledo invariant on smooth varieties of general type

Vincent Jf Koziarz (1) , Julien Maubon (1)

1 IECN - Institut Élie Cartan de Nancy

We propose a definition of the Toledo invariant for representations of fundamental groups of smooth varieties of general type into semisimple Lie groups of Hermitian type. This definition allows to generalize the results known in the classical case of representations of complex hyperbolic lattices to this new setting: assuming that the rank of the target Lie group is not greater than two, we prove that the Toledo invariant satisfies a Milnor-Wood type inequality and we characterize the corresponding maximal representations.

Mots clés: Representation; fundamental group; variety of general type; Toledo invariant; Higgs bundles; Hermitian symmetric spaces

Domaines: Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Vincent Jf Koziarz, Julien Maubon. The Toledo invariant on smooth varieties of general type. 2008. ⟨hal-00334523⟩