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Variétés Rationnellement Connexes: Aspects Géométriques et Arithmétiques
 
L. Bonavero Université de Grenoble 1, Saint-Martin d’Hères, France
B. Hassett Rice University, Houston, TX
J. M. Starr Stony Brook University, Stony Brook, NY
O. Wittenberg Écolé Normale Supérieure, Paris, France
A publication of the Société Mathématique de France
Varietes Rationnellement Connexes: Aspects Geometriques et Arithmetiques
Softcover ISBN:  978-2-85629-339-3
Product Code:  PASY/31
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
Varietes Rationnellement Connexes: Aspects Geometriques et Arithmetiques
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Variétés Rationnellement Connexes: Aspects Géométriques et Arithmétiques
L. Bonavero Université de Grenoble 1, Saint-Martin d’Hères, France
B. Hassett Rice University, Houston, TX
J. M. Starr Stony Brook University, Stony Brook, NY
O. Wittenberg Écolé Normale Supérieure, Paris, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-339-3
Product Code:  PASY/31
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Panoramas et Synthèses
    Volume: 312010; 221 pp
    MSC: Primary 11; 12; 14;

    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.

    Readership

    Graduate students and research mathematicians.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 312010; 221 pp
MSC: Primary 11; 12; 14;

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.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.