On the automorphisms of compact Kähler manifolds | Vidéo | Carmin.tv

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On the automorphisms of compact Kähler manifolds

By Tien-Cuong Dinh

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.

Information about the video

Date of recording 17/10/2022
Date of publication 16/11/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19969103
Cite this video Dinh, Tien-Cuong (17/10/2022). 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

Domain(s)

Bibliography

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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