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H 2 Rationality of Fano 3-folds over non-closed fields

Auteurs : Kuznetsov, Alexander (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... Geometrically rational Fano 3-folds Rationality criterion for Fano 3-folds Intermediate Jacobians General rationality criterion Twister intermediate Jacobians Criterion of Benoist-Wittenberg

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 :
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

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 21/10/2019 Date de captation : 02/10/2019 Collection : Research talks ; Algebraic and Complex Geometry Format : MP4 (.mp4) - HD Durée : 01:06:20 Domaine : Algebraic & Complex Geometry Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2019-10-02_Kuznetsov.mp4 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, ClaireDates : 30/09/2019 - 04/10/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2069.html Citation Data DOI : 10.24350/CIRM.V.19565603 Cite 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

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