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- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1901)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
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)
Authors and Affiliations
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Department of Mathematics, MS 136 Rice University, 77251-1892, Houston, USA
Olivier Wittenberg
Bibliographic Information
Book Title: Intersections de deux quadriques et pinceaux de courbes de genre 1
Book Subtitle: Intersections of two quadrics and pencils of curves of genus 1
Authors: Olivier Wittenberg
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/3-540-69137-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2007
Softcover ISBN: 978-3-540-69137-2Published: 09 February 2007
eBook ISBN: 978-3-540-69141-9Published: 15 February 2007
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 218
Topics: Number Theory, Algebraic Geometry