On the cohomological action of automorphisms of compact Kähler threefolds

Abstract

Extending well-known results on surfaces, we give bounds on the cohomological action of automorphisms of compact Kähler threefolds. More precisely, if the action is virtually unipotent we prove that the norm of $(f^n{)}^{\ast }$ grows at most as $c{n}^4$; in the general case, we give a description of the spectrum of $f^{\ast }$, and bounds on the possible conjugates over $\mathbb{Q}$ of the dynamical degrees ${\lambda }_1(f),{\lambda }_2(f)$. Examples on complex tori show the optimality of the results.

Version accepted for publication on Bulletin de la Société Mathématique de France. We improved the presentation of proofs and the statement of Theorem B, and we added references

References in corpus (1)

• Criteria for the existence of equivariant fibrations on algebraic surfaces and hyperkähler manifolds and equality of automorphisms up to powers - a dynamical viewpoint

Cited by in corpus (2)

• Categorical polynomial entropy
• Polynomial volume growth of quasi-unipotent automorphisms of abelian varieties (with an appendix in collaboration with Chen Jiang)