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On examples of varieties that are not stably rational
Multi angle
Authors : Pirutka, Alena (Author of the conference)
CIRM (Publisher )
14C15 - (Equivariant) Chow groups and rings; motives
14M20 - Rational and unirational varieties
14E08 - Rationality questions
CIRM (Publisher )
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Abstract :
A variety X is stably rational if a product of X and some projective space is rational. There exists examples of stably rational non rational complex varieties. In this talk we will discuss recent series of examples of varieties, which are not stably rational and not even retract rational. The proofs involve studying the properties of Chow groups of zero-cycles and the diagonal decomposition. As concrete examples, we will discuss some quartic double solids (C. Voisin), quartic threefolds (a joint work with Colliot-Thélène), some hypersurfaces (Totaro) and others.
MSC Codes : 14C15 - (Equivariant) Chow groups and rings; motives
14M20 - Rational and unirational varieties
14E08 - Rationality questions
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/09/2015 Conference Date : 01/09/2015 Subseries : Research talks arXiv category : Algebraic Geometry ; Number Theory Mathematical Area(s) : Algebraic & Complex Geometry ; Topology ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 01:02:55 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-09-01_Pirutka.mp4 
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Information on the Event
Event Title : Cohomological Methods in the Theory of Algebraic GroupsEvent Organizers : Calmes, Baptiste ; Chernousov, Vladimir ; Karpenko, Nikita Dates : 31/08/2015 - 04/09/2015 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1001.html
Citation Data
DOI : 10.24350/CIRM.V.18824503Cite this video as: Pirutka, Alena (2015). On examples of varieties that are not stably rational. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18824503 URI : http://dx.doi.org/10.24350/CIRM.V.18824503 |
See Also
- [Post-edited] $H^{3}$ non ramifié et cycles de codimension 2 / Author of the conference Colliot-Thélène, Jean-Louis.
- [Multi angle] The rational motivic sphere spectrum and motivic Serre finiteness / Author of the conference Levine, Marc.
- [Multi angle] Decomposition of the diagonal and applications / Author of the conference Totaro, Burt.
- [Multi angle] Subtle Stiefel-Whitney classes and the J-invariant of quadrics / Author of the conference Vishik, Alexander.
- [Multi angle] The rationality problem for forms of moduli spaces of stable marked curves / Author of the conference Reichstein, Zinovy.
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