Let be cubic plane curves meeting in nine points , ..., . If is any cubic containing , ..., , then contains as well. It is related to Gorenstein rings, and is a generalization of Pappus's hexagon theorem and Pascal's theorem.
Cayley-Bacharach Theorem
See also
Pascal's Theorem, Pappus's Hexagon TheoremExplore with Wolfram|Alpha
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 TheoremCite this as:
Weisstein, Eric W. "Cayley-Bacharach Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cayley-BacharachTheorem.html