Intersections de deux quadriques et pinceaux de courbes de genre 1 = Intersections of two quadrics and pencils of curves of genus 1 /
Wittenberg, Olivier.
Intersections de deux quadriques et pinceaux de courbes de genre 1 = Intersections of two quadrics and pencils of curves of genus 1 / Intersections of two quadrics and pencils of curves of genus 1 Olivier Wittenberg. - Berlin ; New York : Springer, ©2007. - 1 online resource (viii, 218 pages) - Lecture notes in mathematics, 1901 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1901. .
Includes bibliographical references (pages 209-213) and index.
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.
Use copy
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].
Electronic reproduction.
[Place of publication not identified] :
HathiTrust Digital Library,
2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
In French, supplemented with an introduction in English.
9783540691419 3540691413 3540691375 9783540691372
10.1007/3-540-69137-5 doi
978-3-540-69137-2 Springer http://www.springerlink.com
98227730X DE-101
Quartic surfaces.
Quadrics.
Matrix pencils.
Geometry, Algebraic.
Géométrie algébrique.
Surfaces quartiques.
Quadriques.
Faisceaux de matrices.
MATHEMATICS--Geometry--Algebraic.
Geometry, Algebraic.
Quartic surfaces.
Quadrics.
Matrix pencils.
Cuádricas
Geometría algebraica
Geometry, Algebraic
Matrix pencils
Quadrics
Quartic surfaces
Algebraïsche meetkunde.
Diofantische analyse.
Superfícies algébricas.
Geometria algébrica.
Geometry, Algebraic.
Arithmetical algebraic geometry.
QA564 / .W58 2007eb
516.3/5
Intersections de deux quadriques et pinceaux de courbes de genre 1 = Intersections of two quadrics and pencils of curves of genus 1 / Intersections of two quadrics and pencils of curves of genus 1 Olivier Wittenberg. - Berlin ; New York : Springer, ©2007. - 1 online resource (viii, 218 pages) - Lecture notes in mathematics, 1901 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1901. .
Includes bibliographical references (pages 209-213) and index.
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.
Use copy
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].
Electronic reproduction.
[Place of publication not identified] :
HathiTrust Digital Library,
2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
In French, supplemented with an introduction in English.
9783540691419 3540691413 3540691375 9783540691372
10.1007/3-540-69137-5 doi
978-3-540-69137-2 Springer http://www.springerlink.com
98227730X DE-101
Quartic surfaces.
Quadrics.
Matrix pencils.
Geometry, Algebraic.
Géométrie algébrique.
Surfaces quartiques.
Quadriques.
Faisceaux de matrices.
MATHEMATICS--Geometry--Algebraic.
Geometry, Algebraic.
Quartic surfaces.
Quadrics.
Matrix pencils.
Cuádricas
Geometría algebraica
Geometry, Algebraic
Matrix pencils
Quadrics
Quartic surfaces
Algebraïsche meetkunde.
Diofantische analyse.
Superfícies algébricas.
Geometria algébrica.
Geometry, Algebraic.
Arithmetical algebraic geometry.
QA564 / .W58 2007eb
516.3/5