linear condition). It can be shown that the dimension is exactly two if no four of the points are collinear and no seven points lie on a conic. The Cayley–Bacharach theorem can be deduced from this fact. See also Linear system of divisors References Footnotes Bibliography Michel Chasles, Traité des sections coniques, Gauthier-Villars, Paris, 1885. Edward D. Davis, Anthony V. Geramita, and Ferruccio Orecchia, Gorenstein algebras and Cayley–Bacharach theorem, Proceedings of the American Mathematical Society 93 (1985), 593–597. David Eisenbud, Mark Green, and Joe Harris, Cayley–Bacharach theorems and conjectures, Bulletin of the American Mathematical Society 33 (1996), no. 3, 295—324. Algebraic curves Theorems in projective geometry Theorems in algebraic geometry