Automorphism groups of positive entropy on projective threefolds
Frederic Campana, Fei Wang, De-Qi Zhang

TL;DR
This paper investigates the structure of automorphism groups with positive entropy on projective threefolds, revealing their algebraic properties and conditions under which the threefolds are complex tori.
Contribution
It establishes a connection between automorphism groups of positive entropy and semi-simple algebraic groups, and characterizes when threefolds are complex tori based on group actions.
Findings
Automorphism groups modulo null entropy are Zariski-dense in semi-simple real algebraic groups.
If the automorphism group is almost abelian with positive rank and the kernel is infinite, the threefold is a complex torus.
The results apply to minimal threefolds and relate group actions to geometric structures.
Abstract
We prove two results about the natural representation of a group G of automorphisms of a normal projective threefold X on its second cohomology. We show that if X is minimal then G, modulo a normal subgroup of null entropy, is embedded as a Zariski-dense subset in a semi-simple real linear algebraic group of real rank < 3. Next, we show that X is a complex torus if the image of G is an almost abelian group of positive rank and the kernel is infinite, unless X is equivariantly non-trivially fibred.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology
