Abstract: |
(Joint with T.-C. Dinh, K. Oguiso, and D.-Q. Zhang) Let X be a compact Kähler manifold and let f be an automorphism of X (or more generally, a solvable group G acting on X). Given these data, we will introduce some filtrations on the space H^{1,1}(X) of (1,1)-classes of X, which capture the trade-off between the positivity of Kähler classes and the negativity arising from (mixed) Hodge-Riemann relations. We will then explain how the fundamental properties of these filtrations lead to new upper bounds of various dynamical invariants, such as the derived length of G among others, only in terms of the dimension of X. |