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The decomposition theorem: the smooth case

By Arnaud Beauville

Appears in collection : Jean-Morlet Chair 2020 - Workshop: Varieties with Trivial Canonical Class / Chaire Jean-Morlet 2020 - Workshop: Variétés de la classe canonique triviale

The decomposition theorem gives some insight on the structure of compact Kähler manifolds with trivial first Chern class. In the first part of the talk I will try to summarize the history of the problem, from the Calabi conjecture to its proof by Yau; in the second part I will explain why the result is an easy consequence of Yau's theorem.

Information about the video

Date of recording 07/04/2020
Date of publication 10/04/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19627603
Cite this video Beauville, Arnaud (07/04/2020). The decomposition theorem: the smooth case. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19627603
URL https://dx.doi.org/10.24350/CIRM.V.19627603

Domain(s)

Algebraic Geometry

Bibliography

Arnaud Beauville. Variétés Kähleriennes dont la première classe de Chern est nulle. J. Differential Geom. 18 (1983), no. 4, 755–782 (1984). - http://dx.doi.org/10.4310/jdg/1214438181
Daniel Greb; Stefan Kebekus; Thomas Peternell. Singular spaces with trivial canonical class. Minimal models and extremal rays (Kyoto, 2011), 67–113, Adv. Stud. Pure Math., 70, Math. Soc. Japan, [Tokyo], 2016. - http://dx.doi.org/10.2969/aspm/07010067
Stéphane Druel. A decomposition theorem for singular spaces with trivial canonical class of dimension at most five. Invent. Math. 211 (2018), no. 1, 245–296. - https://doi.org/10.1007/s00222-017-0748-y
Stéphane Druel; Henri Guenancia. A decomposition theorem for smoothable varieties with trivial canonical class. J. Éc. polytech. Math. 5 (2018), 117–147. - https://doi.org/10.5802/jep.65
aniel Greb; Henri Guenancia; Stefan Kebekus. Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups. Geom. Topol. 23 (2019), no. 4, 2051–2124. - https://doi.org/10.2140/gt.2019.23.2051
Andreas Höring; Thomas Peternell. Algebraic integrability of foliations with numerically trivial canonical bundle. Invent. Math. 216 (2019), no. 2, 395–419. - https://doi.org/10.1007/s00222-018-00853-2
PEREIRA, Jorge Vitório et TOUZET, Frédéric. Foliations with vanishing Chern classes. Bulletin of the Brazilian Mathematical Society, New Series, 2013, vol. 44, no 4, p. 731-754 - https://doi.org/10.1007/s00574-013-0032-8
GUENANCIA, Henri, Semistability of the tangent sheaf of singular varieties. Algebr. Geom. 3 (2016), no. 5, 508–542. - https://doi.org/10.14231/AG-2016-024

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2250/Slides/Arnaud-Beauville.pdf

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