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On the automorphisms of compact Kähler manifolds
Multi angle
Authors : Dinh, Tien-Cuong (Author of the conference)
CIRM (Publisher )
14J50 - Automorphisms of surfaces and higher-dimensional varieties
32H50 - Iteration problems
32M05 - Complex Lie groups, automorphism groups of complex spaces, See also {22E10}
37B40 - Topological entropy
CIRM (Publisher )
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Abstract :
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.
Keywords : automorphisms of compact Kähler manifolds; zero entropy automorphisms; dynamical filtrations; polynomial growth; derived length
MSC Codes : Keywords : automorphisms of compact Kähler manifolds; zero entropy automorphisms; dynamical filtrations; polynomial growth; derived length
14J50 - Automorphisms of surfaces and higher-dimensional varieties
32H50 - Iteration problems
32M05 - Complex Lie groups, automorphism groups of complex spaces, See also {22E10}
37B40 - Topological entropy
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 16/11/2022 Conference Date : 17/10/2022 Subseries : Research talks arXiv category : Complex Variables ; Dynamical Systems Mathematical Area(s) : Analysis and its Applications ; Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 00:47:46 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-10-17_Dinh.mp4 
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Information on the Event
Event Title : Complex Geometry, Dynamical Systems and Foliation Theory / Géométrie complexe, systèmes dynamiques et théorie de feuilletagesEvent Organizers : Marinescu, George ; Nguyên, Viêt Anh ; Wulcan, Elizabeth Dates : 17/10/2022 - 21/10/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2639.html
Citation Data
DOI : 10.24350/CIRM.V.19969103Cite this video as: Dinh, Tien-Cuong (2022). On the automorphisms of compact Kähler manifolds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19969103 URI : http://dx.doi.org/10.24350/CIRM.V.19969103 |
See Also
- [Multi angle] New solution of a problem of Kolmogorov on width asymptotics in holomorphic function spaces / Author of the conference Nivoche, Stéphanie.
- [Multi angle] Formal principle for rational curves in complex threefolds / Author of the conference Hwang, Jun-Muk.
- [Multi angle] On the metric structure of section rings / Author of the conference Finski, Siarhei.
- [Multi angle] Extension of quasiplurisubharmonic functions / Author of the conference Coman, Dan.
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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