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- Title
F.~S.~Macaulay: From plane curves to Gorenstein rings.
- Authors
Eisenbud, David; Gray, Jeremy
- Abstract
Francis Sowerby Macaulay began his career working on Brill and Noether's theory of algebraic plane curves and their interpretation of the Riemann–Roch and Cayley–Bacharach theorems; in fact it is Macaulay who first stated and proved the modern form of the Cayley–Bacharach theorem. Later in his career Macaulay developed ideas and results that have become important in modern commutative algebra, such as the notions of unmixedness, perfection (the Cohen–Macaulay property), and super-perfection (the Gorenstein property), work that was appreciated by Emmy Noether and the people around her. He also discovered results that are now fundamental in the theory of linkage, but this work was forgotten and independently rediscovered much later. The name of a computer algebra program (now Macaulay2) recognizes that much of his work is based on examples created by refined computation. Though he never spoke of the connection, the threads of Macaulay's work lead directly from the problems on plane curves to his later theorems. In this paper we will explain what Macaulay did, and how his results are connected.
- Subjects
GORENSTEIN rings; ABSTRACT algebra; COMMUTATIVE algebra; ALGEBRAIC curves; PLANE curves; COMPUTER software
- Publication
Bulletin (New Series) of the American Mathematical Society, 2023, Vol 60, Issue 3, p371
- ISSN
0273-0979
- Publication type
Article
- DOI
10.1090/bull/1787