Max Noether's theorem

In mathematics, Max Noether's theorem in algebraic geometry may refer to at least two results.

Max Noether's residual intersection theorem is a result on algebraic curves in the projective plane, on the residual sets of intersections.

There is another Max Noether theorem on curves lying on algebraic surfaces, which are hypersurfaces in P³. or more generally complete intersections. It states that, for degree at least four for hypersurfaces, the generic such surface has no curve on it apart from the hyperplane section. In more modern language, the Picard group is infinite cyclic, other than for a short list of degrees.