On the virtual invariants of zero entropy groups of compact Kahler manifolds
Journal
Pure and Applied Mathematics Quarterly
Journal Volume
22
Journal Issue
1
Start Page
99
End Page
127
ISSN
1558-8599
1558-8602
Date Issued
2026
Author(s)
Abstract
Let X be a compact Kähler manifold. We study subgroups G ≤ Aut(X) of biholomorphic automorphisms of zero entropy when Aut0 (X) is compact (e.g. when Aut0 (X) is trivial). We show that the virtual derived length ℓvir (G) of G satisfies ℓvir (G) ≤ dim X − κ(X), where κ(X) is the Kodaira dimension of X. Modulo the main conjecture of our previous work concerning the essential nilpotency class, we obtain the same upper bound cvir (G) ≤ dim X − κ(X) for the virtual nilpotency class cvir (G), together with a geometric description of G ↺ X when the equality holds.
Publisher
International Press of Boston
Type
journal article