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Cayley-Bacharach Theorem

Let X_1,X_2 subset P^2 be cubic plane curves meeting in nine points p_1, ..., p_9. If X subset P^2 is any cubic containing p_1, ..., p_8, then X contains p_9 as well. It is related to Gorenstein rings, and is a generalization of Pappus's hexagon theorem and Pascal's theorem.

See also

Pascal's Theorem, Pappus's Hexagon Theorem

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References

Eisenbud, D.; Green, M.; and Harris, J. "Cayley-Bacharach Theorems and Conjectures." Bull. Amer. Math. Soc. 33, 295-324, 1996.

Referenced on Wolfram|Alpha

Cayley-Bacharach Theorem

Cite this as:

Weisstein, Eric W. "Cayley-Bacharach Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Cayley-BacharachTheorem.html

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