English
Rationality of Fano 3-folds over non-closed fields
Post-edited
Auteurs : Kuznetsov, Alexander (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 21/10/2019 Date de captation : 02/10/2019 Sous collection : Research talks arXiv category : Algebraic Geometry Domaine : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Durée : 01:06:20 Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-02_Kuznetsov.mp4 
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Informations sur la Rencontre
Nom de la rencontre : The Geometry of Algebraic Varieties / Géométrie des variétés algébriquesOrganisateurs de la rencontre : Benoist, Olivier ; Jiang, Zhi ; Voisin, Claire Dates : 30/09/2019 - 04/10/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2069.html
Données de citation
DOI : 10.24350/CIRM.V.19565603Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Cayley-Bacharach theorems with excess vanishing / Auteur de la Conférence Lazarsfeld, Robert.
- [Multi angle] Algebraic and arithmetic aspects of twistor spaces / Auteur de la Conférence Huybrechts, Daniel.
- [Multi angle] Gushel-Mukai varieties and their periods / Auteur de la Conférence Debarre, Olivier.
- [Multi angle] Special rational fibrations in Fano 4-folds / Auteur de la Conférence Casagrande, Cinzia.
Bibliographie
