Reiss relation

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.

Statement

If C is a complex plane curve given by the zeros of a polynomial f 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_x, f_xy and so on stand for partial derivatives of f .
This can also be written as
where κ is the curvature of the curve C and θ is the angle its tangent line makes with L, and the sum is again over the points of intersection of C and L.