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
 * $$\sum\frac{f_{xx}f_y^2-2f_{xy}f_xf_y+f_{yy}f_x^2}{f_y^3}=0$$

where the sum is over the points of intersection of C and L, and fx, fxy and so on stand for partial derivatives of f. This can also be written as
 * $$\sum\frac{\kappa}{\sin(\theta)^3}=0$$

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.