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Oberseminar WiSe 2011/12 Zusammenfassung des Vortrags von De-Qi Zhang (Singapore)

Automorphisms of positive entropy on compact Kahler manifolds

We show that a minimal compact Kahler manifold (or minimal normal projective variety) X of dimension n > 2 has at most n -1 independent commuting (modulo elements of null entropy) automorphisms of positive entropy and the maximality n -1 occurs only when X is a quotient of a compact torus.

We also propose an open question: if the representation G | NSR(X) on the Néron-Severi group is embedded as a Zariski-dense subset in a real rank n -1 semi-simple group, then is X birational to a quotient of an abelian variety?