Elliptic rational functions

Pure mathematics

Operating system

Elliptic curve

Computer science

Section (typography)

Mathematics

Quarter period

Algebra over a field

Advanced studies in pure mathematics

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.

Elliptic surfaces