Seminar Algebra and Geometry: Federico Lo Bianco (Rennes)

Cohomological action of automorphisms of compact Kaehler threefolds

An automorphism f acting on a complex projective (or, more generally, compact Kaehler) manifold X induces by pull-back a linear isomorphism f^* of the cohomology of X. The study of the possible isomorphisms that can be realized this way is interesting per se and also has important applications in the study of the dynamics of f: for example, the topological entropy of f, measuring the chaos created by repeatedly applying f, can be recovered from the eigenvalues of f^*. If X is a surface the situation is well understood: if f^* is not of finite order, then either it is virtually unipotent with only one non-trivial Jordan block of dimension 3, or semi-simple with only two eigenvalues with module different than 1. I will present the similar results I obtained with Cantat for threefolds and show their optimality with examples on complex tori.

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