English
The decomposition theorem: the smooth case
Virtualconference
Auteurs : Beauville, Arnaud (Auteur de la conférence)
CIRM (Editeur )
14J32 - Calabi-Yau manifolds
53C26 - Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2250/Slides/Arnaud-Beauville.pdf
CIRM (Editeur )
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Résumé :
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.
Mots-Clés : Calabi conjecture; Calabi-Yau manifolds; hyperkähler manifolds
Codes MSC : Mots-Clés : Calabi conjecture; Calabi-Yau manifolds; hyperkähler manifolds
14J32 - Calabi-Yau manifolds
53C26 - Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2250/Slides/Arnaud-Beauville.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 10/04/2020 Date de Captation : 07/04/2020 Sous Collection : Research talks Catégorie arXiv : Algebraic Geometry Domaine(s) : Géométrie Complexe & géométrie Algébrique Format : MP4 (.mp4) - HD Durée : 00:35:37 Audience : Chercheurs Download : https://videos.cirm-math.fr/2020-04-06_Beauville.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Jean-Morlet Chair 2020 - Workshop: Varieties with Trivial Canonical Class / Chaire Jean-Morlet 2020 - Workshop: Variétés de la classe canonique trivialeOrganisateurs de la Rencontre : Loray, Frank ; Pereira, Jorge Vitório ; Rousseau, Erwan Dates : 06/04/2020 - 17/04/2020 Année de la rencontre : 2020 URL de la Rencontre : https://www.chairejeanmorlet.com/2250.html
Données de citation
DOI : 10.24350/CIRM.V.19627603Citer cette vidéo: Beauville, Arnaud (2020). The decomposition theorem: the smooth case. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19627603 URI : http://dx.doi.org/10.24350/CIRM.V.19627603 |
Voir Aussi
- [Virtualconference] Varieties with Trivial Canonical Class: problem session / Animateur Pereira, Jorge Vitório.
- [Virtualconference] Varieties with Trivial Canonical Class: discussion session / Animateur Pereira, Jorge Vitório.
- [Virtualconference] Interview at CIRM: Jorge Vitório Pereira / Personne interviewée Pereira, Jorge Vitório ; Intervieweur Vareilles, Stéphanie.
- [Virtualconference] Holonomy of singular Ricci-flat metrics / Auteur de la conférence Guenancia, Henri.
- [Virtualconference] A splitting theorem / Auteur de la conférence Druel, Stéphane.
- [Virtualconference] Rational curves and contraction loci on symplectic manifolds / Auteur de la conférence Amerik, Ekaterina.
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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