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"("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""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" .