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Stably irrational hypersurfaces of small slopes
Multi angle
Authors : Schreieder, Stefan (Author of the conference)
CIRM (Publisher )
14C30 - Transcendental methods, Hodge theory, Hodge conjecture
14J70 - Algebraic hypersurfaces
14M20 - Rational and unirational varieties
14E08 - Rationality questions
CIRM (Publisher )
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Abstract :
We show that over any uncountable field of characteristic different from two, a very general hypersurface of dimension $n > 2$ and degree at least $log_2 (n) + 2$ is not stably rational. This significantly improves earlier results of Kollár and Totaro. As a byproduct of our proof, we obtain new counterexamples to the integral Hodge conjecture, answering a question of Voisin and Colliot-Thélène – Voisin.
Keywords : hypersurfaces; rationality problem; stable rationality; integral Hodge conjecture; unramified cohomology
MSC Codes : Keywords : hypersurfaces; rationality problem; stable rationality; integral Hodge conjecture; unramified cohomology
14C30 - Transcendental methods, Hodge theory, Hodge conjecture
14J70 - Algebraic hypersurfaces
14M20 - Rational and unirational varieties
14E08 - Rationality questions
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 21/02/2019 Conference Date : 14/02/2019 Subseries : Research talks arXiv category : Algebraic Geometry ; Complex Variables Mathematical Area(s) : Algebraic & Complex Geometry ; Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 01:02:35 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-02-14_Schreieder.mp4 
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Information on the Event
Event Title : Birational geometry and Hodge theory / Géométrie birationnelle et théorie de HodgeEvent Organizers : Claudon, Benoît ; Höring, Andreas ; Rousseau, Erwan ; Taji, Behrouz Dates : 11/02/2019 - 15/02/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2101.html
Citation Data
DOI : 10.24350/CIRM.V.19494303Cite this video as: Schreieder, Stefan (2019). Stably irrational hypersurfaces of small slopes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19494303 URI : http://dx.doi.org/10.24350/CIRM.V.19494303 |
See Also
- [Multi angle] On the B-Semiampleness Conjecture / Author of the conference Floris, Enrica.
- [Multi angle] Arithmetic of rank one local systems / Author of the conference Esnault, Hélène.
- [Multi angle] Absolute sets and the Decomposition Theorem / Author of the conference Budur, Nero.
- [Post-edited] On the Lüroth problem for real varieties / Author of the conference Benoist, Olivier.
Bibliography
- Schreieder, S. (2018). Stably irrational hypersurfaces of small slopes.
