Derived length of zero entropy groups acting on compact Kahler manifolds

Tien-Cuong Dinh, Keiji Oguiso, De-Qi Zhang

Published 2018-10-11Version 1

Let X be a compact Kahler manifold of dimension n. Let G be a group of zero entropy automorphisms of X. Let G0 be the set of elements in G which are isotopic to the identity. We prove that after replacing G by a suitable finite-index subgroup, G/G0 is a unipotent group of derived length at most n-1. This is a corollary of an optimal upper bound of length involving the Kodaira dimension of X. We also study the algebro-geometric structure of X when it admits a group action with maximal derived length n-1.