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The decomposition theorem: the smooth case

De Arnaud Beauville

Apparaît dans la 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.

Informations sur la vidéo

Données de citation

  • DOI 10.24350/CIRM.V.19627603
  • Citer cette vidéo 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

Bibliographie

  • 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

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