Elliptic Surfaces
Matthias Schuett, Tetsuji Shioda
TL;DR
This survey provides a comprehensive overview of elliptic surfaces with section, focusing on rational elliptic surfaces and elliptic K3 surfaces, including their theory, examples, and arithmetic properties.
Contribution
It offers a detailed review of the theory of elliptic surfaces, emphasizing Mordell-Weil lattices and arithmetic questions, with numerous examples.
Findings
Extensive classification of elliptic surfaces with section
Insights into Mordell-Weil lattices and their arithmetic properties
Compilation of key examples of rational elliptic and K3 surfaces
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds