In arithmetic geometry, the Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines whether a given set of sections[further explanation needed] provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S, where S is isomorphic to the projective line.[1]
The algorithm was first published in the 1979 article "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker[2] and was later named the "Cox–Zucker machine" by Charles Schwartz in 1984.[1]
Name origin
editThe name sounds similar to the obscenity "cocksucker". This was a deliberate choice by Cox and Zucker, who, as first-year graduate students at Princeton University in 1970, conceived of the idea of coauthoring a paper for the express purpose of enabling this joke. They followed through on it five years later, as members of the faculty at Rutgers, the State University of New Jersey.[3] As Cox explained in a memorial tribute to Zucker in Notices of the American Mathematical Society in 2021: "A few weeks after we met, we realized that we had to write a joint paper because the combination of our last names, in the usual alphabetical order, is remarkably obscene."[3]
See also
editReferences
edit
- ^ a b Schwartz, Charles F. (1984). "A Mordell–Weil Group of Rank 8, and a Subgroup of Finite Index". Nagoya Mathematical Journal. 93: 17–26. doi:10.1017/S0027763000020705. MR 0738915. Zbl 0504.14031.
- ^ Cox, David A.; Zucker, Steven (1979-02-01). "Intersection numbers of sections of elliptic surfaces". Inventiones Mathematicae. 53 (1): 1–44. Bibcode:1979InMat..53....1C. doi:10.1007/BF01403189. ISSN 0020-9910. S2CID 15130840.
- ^ a b Cox, David (1 August 2021). "Remembering Steve Zucker" (PDF). Notices of the American Mathematical Society. 68 (7): 1162. doi:10.1090/noti2310..