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Bulletin of the American Mathematical Society

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



Cayley-Bacharach theorems and conjectures

Authors: David Eisenbud, Mark Green and Joe Harris
Journal: Bull. Amer. Math. Soc. 33 (1996), 295-324
MSC (1991): Primary 14N05, 14H05, 14-02; Secondary 13-03, 13H10
MathSciNet review: 1376653
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Abstract: 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

Mark Green
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555

Joe Harris
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138-2901

Received by editor(s): March 24, 1995
Received by editor(s) in revised form: November 3, 1995
Article copyright: © Copyright 1996 American Mathematical Society