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Intersections de deux quadriques et pinceaux de courbes de genre 1: Intersections of two quadrics and pencils of curves of genus 1 de Olivier Wittenberg

Intersections de deux quadriques et pinceaux de courbes de genre 1: Intersections of two quadrics and pencils of curves of genus 1: Lecture Notes in Mathematics, cartea 1901

Autor Olivier Wittenberg
fr Limba Franceză Paperback – 9 feb 2007
Cet ouvrage est consacré à l'arithmétique des surfaces fibrées en courbes de genre 1 au-dessus de la droite projective, et à l'arithmétique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une technique permettant d'étudier les points rationnels des pinceaux de courbes de genre 1. La première moitié de l'ouvrage reprend et développe cette technique ainsi que ses généralisations ultérieures. La seconde moitié, qui repose sur la première, porte sur les surfaces de del Pezzo de degré 4 et sur les intersections de deux quadriques de dimension supérieure; les résultats annoncés dans [C. R. Math. Acad. Sci. Paris 342 (2006), no. 4, 223--227] y sont démontrés.
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Specificații

ISBN-13: 9783540691372
ISBN-10: 3540691375
Pagini: 232
Ilustrații: VIII, 218 p. Avec online files/update.
Dimensiuni: 155 x 235 x 12 mm
Greutate: 0.45 kg
Ediția:2007
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

Arithmétique des pinceaux semi-stables de courbes de genre 1 (première partie).- Arithmétique des pinceaux semi-stables de courbes de genre 1 (seconde partie).- Principe de Hasse pour les surfaces de del Pezzo de degré 4.

Recenzii

From the reviews:
"The monograph under review grew out of the author’s Ph.D thesis. … The monograph is written in extremely careful manner. … There are two introductions: the English one makes emphasis on the general context, whereas the French one contains more technical descriptions and references. To sum up, the monograph can be recommended to everyone interested in the state of the art of methods and results concerning arithmetic of rational varieties." (Boris Kunyavskii, Zentralblatt MATH, Vol. 1122 (24), 2007)

Textul de pe ultima copertă

Cet ouvrage est consacré à l'arithmétique des surfaces fibrées en courbes de genre 1 au-dessus de la droite projective, et à l'arithmétique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une technique permettant d'étudier les points rationnels des pinceaux de courbes de genre 1. La première moitié de l'ouvrage reprend et développe cette technique ainsi que ses généralisations ultérieures. La seconde moitié, qui repose sur la première, porte sur les surfaces de del Pezzo de degré 4 et sur les intersections de deux quadriques de dimension supérieure; les résultats annoncés dans [C. R. Math. Acad. Sci. Paris 342 (2006), no. 4, 223--227] y sont démontrés.
This research monograph focuses on the arithmetic, over number fields, of
surfaces fibred into curves of genus 1 over the projective line, and of
intersections of two quadrics in projective space.  The first half contains a
complete account of the technique initiated by Swinnerton-Dyer in 1993 for
studying rational points on pencils of curves of genus 1, while incorporating
and generalising most of its subsequent refinements.  The second half, which
builds upon the first, is devoted to quartic del Pezzo surfaces and
higher-dimensional intersections of two quadrics.  It culminates in the proof
of the results announced in [C. R. Math. Acad. Sci. Paris 342 (2006), no. 4,
223--227].

Caracteristici

Includes supplementary material: sn.pub/extras