no. 3
On the cohomological action of automorphisms of compact Kähler threefolds
[Sur l’action cohomologique des automorphismes des variétés compactes kähleriennes de dimension 3]
Lo Bianco, F.1
1 Institut de Mathématiques de Marseille, University of Aix-Marseille, Centre de Mathématiques et Informatique (CMI), Technopôle Château-Gombert, Marseille (France)
Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 3, pp. 469-514

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 (fn)* grows at most as cn4; in the general case, we give a description of the spectrum of f*, and bounds on the possible conjugates over ℚ of the dynamical degrees λ1(f),λ2(f). Examples on compact complex tori show the optimality of the results.

Nous étendons des résultats bien connus sur l’action en cohomologie des automorphismes des surfaces aux variétés compactes Kähler de dimension 3. Plus précisément, si l’action est virtuellement unipotente nous montrons que la norme de (fn)* croît au plus comme cn4 ; dans le cas général, nous donnons une description du spectre de f* et des bornes sur les possibles conjugués sur ℚ des degrés dynamiques λ1(f),λ2(f). Des exemples sur les tores complexes compacts montrent l’optimalité de ces résultats.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.24033/bsmf.2790
Classification : 14J30, 14J50, 32Q15
Keywords: Complex geometry, automorphisms of Kähler manifolds, dynamical degrees
Mots-clés : Géométrie complexe, automorphismes de variétés kählériennes, degrés dynamiques

Lo Bianco, F. 1

1 Institut de Mathématiques de Marseille, University of Aix-Marseille, Centre de Mathématiques et Informatique (CMI), Technopôle Château-Gombert, Marseille (France) 
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Lo Bianco, F. On the cohomological action of automorphisms of compact Kähler threefolds. Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 3, pp. 469-514. doi: 10.24033/bsmf.2790

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