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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Cayley-Bacharach theorems and conjectures
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by David Eisenbud, Mark Green and Joe Harris PDF
Bull. Amer. Math. Soc. 33 (1996), 295-324 Request permission


A theorem of Pappus of Alexandria, proved in the fourth century A.D., began a long development in algebraic geometry. In its changing expressions one can see reflected the changing concerns of the field, from synthetic geometry to projective plane curves to Riemann surfaces to the modern development of schemes and duality. We survey this development historically and use it to motivate a brief treatment of a part of duality theory. We then explain one of the modern developments arising from it, a series of conjectures about the linear conditions imposed by a set of points in projective space on the forms that vanish on them. We give a proof of the conjectures in a new special case.
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Additional Information
  • David Eisenbud
  • Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254-9110
  • MR Author ID: 62330
  • ORCID: 0000-0002-5418-5579
  • Email:
  • Mark Green
  • Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555
  • MR Author ID: 76530
  • Email:
  • Joe Harris
  • Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138-2901
  • Email:
  • Received by editor(s): March 24, 1995
  • Received by editor(s) in revised form: November 3, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 33 (1996), 295-324
  • MSC (1991): Primary 14N05, 14H05, 14-02; Secondary 13-03, 13H10
  • DOI:
  • MathSciNet review: 1376653