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Cox–Zucker machine - mklabgr - 08-10-2026
Cox–Zucker machine
Summary
The Cox–Zucker machine is an algorithm in arithmetic geometry developed by David A. Cox and Steven Zucker for studying elliptic surfaces, particularly when the base curve is the projective line. It determines whether a given collection of sections—which can be viewed as choosing a point on each fiber of the surface—forms a basis, up to torsion, for the surface’s Mordell–Weil group.
The underlying method was introduced in their 1979 paper on intersection numbers of sections of elliptic surfaces, while the name “Cox–Zucker machine” was coined by Charles Schwartz in 1984. The name itself is also a mathematical joke, since “Cox–Zucker” sounds very similar to an English obscenity.
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