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Rationality of Fano 3-folds over non-closed fields
Post-edited
Authors : Kuznetsov, Alexander (Author of the conference)
CIRM (Publisher )
05-XX - Combinatorics, {For finite fields, See 11Txx}
14J45 - Fano varieties
41-XX - Approximations and expansions [For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx]
62-XX - Statistics
CIRM (Publisher )
Abstract :
In the talk I will discuss rationality criteria for Fano 3-folds of geometric Picard number 1 over a non-closed field $k$ of characteristic 0. Among these there are 8 types of geometrically rational varieties. We prove that in one of these cases any variety of this type is k-rational, in four cases the criterion of rationality is the existence of a $k$-rational point, and in the last three cases the criterion is the existence of a $k$-rational point and a k rational curve of genus 0 and degree 1, 2, and 3 respectively. The last result is based on recent results of Benoist-Wittenberg. This is a joint work with Yuri Prokhorov.
Keywords : rationality questions; Fano 3-folds
MSC Codes : Keywords : rationality questions; Fano 3-folds
05-XX - Combinatorics, {For finite fields, See 11Txx}
14J45 - Fano varieties
41-XX - Approximations and expansions [For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx]
62-XX - Statistics
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 21/10/2019 Conference Date : 02/10/2019 Subseries : Research talks arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:06:20 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-02_Kuznetsov.mp4 
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Information on the Event
Event Title : The Geometry of Algebraic Varieties / Géométrie des variétés algébriquesEvent Organizers : Benoist, Olivier ; Jiang, Zhi ; Voisin, Claire Dates : 30/09/2019 - 04/10/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2069.html
Citation Data
DOI : 10.24350/CIRM.V.19565603Cite this video as: Kuznetsov, Alexander (2019). Rationality of Fano 3-folds over non-closed fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19565603 URI : http://dx.doi.org/10.24350/CIRM.V.19565603 |
See Also
- [Multi angle] Cayley-Bacharach theorems with excess vanishing / Author of the conference Lazarsfeld, Robert.
- [Multi angle] Algebraic and arithmetic aspects of twistor spaces / Author of the conference Huybrechts, Daniel.
- [Multi angle] Gushel-Mukai varieties and their periods / Author of the conference Debarre, Olivier.
- [Multi angle] Special rational fibrations in Fano 4-folds / Author of the conference Casagrande, Cinzia.
Bibliography
