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Appears in collection : Complex Geometry, Dynamical Systems and Foliation Theory / Géométrie complexe, systèmes dynamiques et théorie de feuilletages

The automorphism group of a compact Kähler manifold satisfies Tits alternative: any subgroup either admits a solvable subgroup of finite index or contains a free non-abelian group of two generators (Campana-WangZhang). In the first case, this group cannot be too big. Some algebraic (rational) manifolds with special automorphisms admit infinitely many nonequivalent real forms. This talk is based on my (old and recent) works with F. Hu, H.-Y. Lin, V.-A. Nguyen, K. Oguiso, N. Sibony, X. Yu, D.-Q. Zhang.

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Citation data

  • DOI 10.24350/CIRM.V.19969103
  • Cite this video Dinh Tien-Cuong (10/17/22). On the automorphisms of compact Kähler manifolds. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19969103
  • URL https://dx.doi.org/10.24350/CIRM.V.19969103


  • DINH, Tien-Cuong et SIBONY, Nessim. Groupes commutatifs d'automorphismes d'une variété kählérienne compacte. Duke Mathematical Journal, 2004, vol. 123, no 2, p. 311-328. - http://dx.doi.org/10.1215/S0012-7094-04-12323-1
  • DINH, Tien-Cuong., NGUYEN, Viêt-Anh. The mixed Hodge–Riemann bilinear relations for compact Kähler manifolds. GAFA, Geom. funct. anal. , 2006, vol.16, p. 838–849. - http://dx.doi.org/10.1007/s00039-006-0572-9
  • DINH, Tien-Cuong, HU, Fei, et ZHANG, De-Qi. Compact Kähler manifolds admitting large solvable groups of automorphisms. Advances in Mathematics, 2015, vol. 281, p. 333-352. - https://doi.org/10.1016/j.aim.2015.05.002
  • DINH, Tien-Cuong et OGUISO, Keiji. A surface with discrete and nonfinitely generated automorphism group. Duke Mathematical Journal, 2019, vol. 168, no 6, p. 941-966. - http://dx.doi.org/10.1215/00127094-2018-0054
  • DINH, Tien-Cuong, LIN, Hsueh-Yung, OGUISO, Keiji, et al. Zero entropy automorphisms of compact Kähler manifolds and dynamical filtrations. Geometric and Functional Analysis, 2022, p. 1-27. - http://dx.doi.org/10.1007/s00039-022-00599-3
  • DINH, Tien-Cuong, OGUISO, Keiji, et YU, Xun. Smooth complex projective rational surfaces with infinitely many real forms. arXiv preprint arXiv:2106.05687, 2021. - https://doi.org/10.48550/arXiv.2106.05687

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