English
Rational curves on K3 surfaces
Multi angle
Auteurs : Gounelas, Frank (Auteur de la Conférence)
CIRM (Editeur )
14J28 - $K3$ surfaces and Enriques surfaces
CIRM (Editeur )
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Résumé :
Bogomolov and Mumford proved that every complex projective K3 surface contains a rational curve. Since then, a lot of progress has been made by Bogomolov, Chen, Hassett, Li, Liedtke, Tschinkel and others, towards the stronger statement that any such surface in fact contains infinitely many rational curves. In this talk I will present joint work with Xi Chen and Christian Liedtke completing the remaining cases of this conjecture, reproving some of the main previously known cases more conceptually and extending the result to arbitrary genus in a suitable sense.
Keywords : curves on K3 surfaces; rational curves; deformation of curves
Codes MSC : Keywords : curves on K3 surfaces; rational curves; deformation of curves
14J28 - $K3$ surfaces and Enriques surfaces
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 17/12/2019 Date de captation : 28/11/2019 Sous collection : Research talks arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 00:53:10 Audience : Researchers Download : https://videos.cirm-math.fr/2019-11-28_Gounelas.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Algebraic Geometry and Complex Geometry / Géométrie algébrique et géométrie complexeOrganisateurs de la rencontre : Benoist, Olivier ; Floris, Enrica Dates : 25/11/2019 - 29/11/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2074.html
Données de citation
DOI : 10.24350/CIRM.V.19580803Citer cette vidéo: Gounelas, Frank (2019). Rational curves on K3 surfaces. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19580803 URI : http://dx.doi.org/10.24350/CIRM.V.19580803 |
Voir aussi
- [Multi angle] The essential skeletons of pairs and the geometric P=W conjecture / Auteur de la Conférence Mauri, Mirko.
- [Multi angle] Representation varieties of fundamental groups of complex algebraic varieties and mixed Hodge structures / Auteur de la Conférence Lefèvre, Louis-Clément.
- [ Post-edited] Failure of the Brauer-Manin obstruction for a simply connected fourfold, and an orbifold version of the Mordell theorem / Auteur de la Conférence Kebekus, Stefan.
- [Multi angle] Momentum polytopes of Kähler compact multiplicity-free manifolds / Auteur de la Conférence Cupit-Foutou, Stéphanie.
Bibliographie
- CHEN, Xi, GOUNELAS, Frank, et LIEDTKE, Christian. Curves on K3 surfaces. arXiv preprint arXiv:1907.01207, 2019. - https://arxiv.org/abs/1907.01207
