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On examples of varieties that are not stably rational

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Authors : Pirutka, Alena (Author of the conference)
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

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : 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

Information on the Event

Event Title : Cohomological Methods in the Theory of Algebraic Groups
Event 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.18824503
Cite 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

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