Abstract
This survey paper concerns elliptic surfaces with section. We give a detailed overview of the theory including many examples. Emphasis is placed on rational elliptic surfaces and elliptic K3 surfaces. To this end, we particularly review the theory of Mordell–Weil lattices and address arithmetic questions.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1216.14036
MathSciNet: MR2732092
Digital Object Identifier: 10.2969/aspm/06010051
Subjects:
Primary:
14J27
Secondary:
06B05
,
11G05
,
11G07
,
11G50
,
14J20
,
14J26
,
14J28
Keywords:
Elliptic curve
,
elliptic surface
,
K3 surface
,
Mordell–Weil group
,
Mordell–Weil lattice
,
Néron–Severi group
,
singular fibre
,
Tate algorithm
Rights: Copyright © 2010 Mathematical Society of Japan
