Panoramas et Syntheses
Volume: 31; 2010; 221 pp; Softcover
MSC: Primary 11; 12; 14;
Print ISBN: 978-2-85629-339-3
Product Code: PASY/31
List Price: $60.00
Individual Member Price: $48.00
Variétés Rationnellement Connexes: Aspects Géométriques et ArithmétiquesShare this page
L. Bonavero; B. Hassett; J. M. Starr; O. Wittenberg
A publication of the Société Mathématique de France
Over the last twenty years, rationally connected varieties have played an important role in the classification program of higher dimensional varieties. Over the last ten years, a number of their arithmetic properties have been discovered. It is the goal of this volume to report on many of these advances, as well as on a number of open questions.
This volume gathers the contributions of the four speakers at the CNRS/SMF workshop “Etats de la Recherche”, which was organized by J.-L. Colliot-Thélène, O. Debarre, and A. Höring in Strasbourg in May 2008.
L. Bonavero discusses the fundamental geometric properties of rationally connected varieties and also offers an opening on modern birational classification techniques. O. Wittenberg surveys the arithmetic properties of rationally connected varieties, mostly over local fields and over finite fields (deformation techniques and cohomological techniques). B. Hassett reports on the weak approximation property for families of rationally connected varieties over a complex curve.
The emerging notion of simply rationally connected variety is at the heart of J. Starr's contribution. Starr's paper starts with a study of sections of families of such varieties over a complex surface and culminates with a partly simplified proof of the theorem by de A. J. Jong, J. Starr, and X. He: Serre's Conjecture II for principal homogeneous spaces holds over function fields in two variables over the complex field.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Table of Contents
Table of Contents
Varietes Rationnellement Connexes: Aspects Geometriques et Arithmetiques
Graduate students and research mathematicians.