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Rational curves on K3 surfaces
Multi angle
Authors : Gounelas, Frank (Author of the conference)
CIRM (Publisher )
14J28 - $K3$ surfaces and Enriques surfaces
CIRM (Publisher )
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Abstract :
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
MSC Codes : Keywords : curves on K3 surfaces; rational curves; deformation of curves
14J28 - $K3$ surfaces and Enriques surfaces
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 17/12/2019 Conference Date : 28/11/2019 Subseries : Research talks arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:53:10 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-11-28_Gounelas.mp4 
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Information on the Event
Event Title : Algebraic Geometry and Complex Geometry / Géométrie algébrique et géométrie complexeEvent Organizers : Benoist, Olivier ; Floris, Enrica Dates : 25/11/2019 - 29/11/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2074.html
Citation Data
DOI : 10.24350/CIRM.V.19580803Cite this video as: 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 |
See Also
- [Multi angle] The essential skeletons of pairs and the geometric P=W conjecture / Author of the conference Mauri, Mirko.
- [Multi angle] Representation varieties of fundamental groups of complex algebraic varieties and mixed Hodge structures / Author of the conference Lefèvre, Louis-Clément.
- [Post-edited] Failure of the Brauer-Manin obstruction for a simply connected fourfold, and an orbifold version of the Mordell theorem / Author of the conference Kebekus, Stefan.
- [Multi angle] Momentum polytopes of Kähler compact multiplicity-free manifolds / Author of the conference Cupit-Foutou, Stéphanie.
Bibliography
- CHEN, Xi, GOUNELAS, Frank, et LIEDTKE, Christian. Curves on K3 surfaces. arXiv preprint arXiv:1907.01207, 2019. - https://arxiv.org/abs/1907.01207
