Elliptic Surfaces

2009/07/02 by Matthias Schuett, Tetsuji Shioda, Schuett, Matthias +1 · 3 citations
Mathematics · #06B05 #11G05 #11G07 #11G50 #14J20 #14J26 #14J27 (Primary) #14J28 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0907.0298

openalex publication_date 2009/07/02 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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.

Cited by

• The Arithmetic Geometry of Square-Sided Heron Triangles
• Families of curves in Vinberg representations
• Varieties with representable CH₀-group and a question of Colliot-Thélène

Related

• Geometric and arithmetic aspects of rational elliptic surfaces
• The Geometry and Arithmetic of Elliptic Surfaces
• Sections on certain j=0 elliptic surfaces
• Three lectures on elliptic surfaces and curves of high rank
• Connected components of the moduli of elliptic K3 surfaces