English
Periods of polarized hyperkähler manifolds
Post-edited
Auteurs : Debarre, Olivier (Auteur de la Conférence)
CIRM (Editeur )
14C34 - Torelli problem
14E07 - Birational automorphisms, Cremona group and generalizations
14J50 - Automorphisms of surfaces and higher-dimensional varieties
14J60 - Vector bundles on surfaces and higher-order varieties, and their moduli
CIRM (Editeur )
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| K3 surfaces polarized K3 surfaces period map period domain hyperkähler manifolds period map for hyperkähler manifolds strange duality questions from the audience |
Résumé :
Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly determine the image of this map in some cases. I will explain this result together with a nice application (found by Bayer and Mongardi) to the (almost complete) determination of the image of the period map for cubic fourfolds, hereby partially recovering a result of Laza.
Codes MSC : 14C34 - Torelli problem
14E07 - Birational automorphisms, Cremona group and generalizations
14J50 - Automorphisms of surfaces and higher-dimensional varieties
14J60 - Vector bundles on surfaces and higher-order varieties, and their moduli
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 12/04/2018 Date de captation : 10/04/2018 Sous collection : Research talks arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 00:55:59 Audience : Researchers Download : https://videos.cirm-math.fr/2018-04-10_Debarre.mp4 
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Informations sur la Rencontre
Nom de la rencontre : French-German meeting on complex algebraic geometry / Rencontre franco-allemande en géométrie algébrique complexeOrganisateurs de la rencontre : Greb, Daniel ; Höring, Andreas ; Toma, Matei Dates : 09/04/2018 - 13/04/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1789.html
Données de citation
DOI : 10.24350/CIRM.V.19387903Citer cette vidéo: Debarre, Olivier (2018). Periods of polarized hyperkähler manifolds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19387903 URI : http://dx.doi.org/10.24350/CIRM.V.19387903 |
Voir aussi
- [Multi angle] Gonality and zero-cycles of abelian varieties / Auteur de la Conférence Voisin, Claire.
- [Multi angle] Signature morphisms from the Cremona group / Auteur de la Conférence Zimmermann, Susanna.
- [Multi angle] Nonabelian Hodge correspondences for klt varieties and quasi-etale uniformisation / Auteur de la Conférence Kebekus, Stefan.
- [Multi angle] Improved bounds for the Kobayashi conjecture on generic hyperbolicity / Auteur de la Conférence Demailly, Jean-Pierre.
- [Multi angle] Deformation theory of twistor spaces of K3 surfaces / Auteur de la Conférence Brecan, Ana-Maria.
Bibliographie
- Debarre, O., & Macrì, E. (2017). On the period map for polarized hyperkähler fourfolds.
- Debarre, O. (2018). Hyperkähler manifolds, Lecture notes - http://www.math.ens.fr/~debarre/HKsurvey.pdf
