Elliptic 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.

93 pages; v3: refereed version, some typos corrected

Cited by in corpus (10)

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• The Geometry of Flex Tangents to a Cubic Curve and its Parameterizations
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• Eta Products, BPS States and K3 Surfaces
• F-theory and Heterotic Duality, Weierstrass Models from Wilson lines
• Exact Formulas for Invariants of Hilbert Schemes
• The greatest common valuation of ${\varphi }_n$ and ${\psi }_n^2$ at points on elliptic curves
• Automorphisms of unnodal Enriques surfaces
• Arithmetic geometry of the moduli stack of Weierstrass fibrations over ${\mathbb{P}}^1$