In algebraic geometry, the Reiss relation, introduced by , is a condition on the second-order elements of the points of a plane algebraic curve meeting a given line.
If C is a complex plane curve given by the zeros of a polynomial f(x,y) of two variables, and L is a line meeting C transversely and not meeting C at infinity, then
where the sum is over the points of intersection of C and L, and f<sub>x</sub>, f<sub>xy</sub> and so on stand for partial derivatives of f . This can also be written as
where ú is the curvature of the curve C and ø is the angle its tangent line makes with L, and the sum is again over the points of intersection of C and L .