Hidden Bibliographic Details
| Varying Form of Title: | Intersections of two quadrics and pencils of curves of genus 1
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| ISBN: | 9783540691419
3540691413
3540691375
9783540691372
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| Notes: | Includes bibliographical references (pages 209-213) and index.
Restrictions unspecified
Electronic reproduction. [S.l.] : 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.
digitized 2010 HathiTrust Digital Library committed to preserve
Print version record.
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| Summary: | 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].
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| Other form: | Print version: Wittenberg, Olivier. Intersections de deux quadriques et pinceaux de courbes de genre 1 =. Berlin ; New York : Springer, ©2007 9783540691372
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| Standard no.: | 10.1007/3-540-69137-5
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