Hessian Covariant

$$H\equiv\vert aa'a''\vert a_{x^{n-2}}a'_{x^{n-2}}a''_{x^{n-2}}=0.$$

The nonsingular inflections of a curve are its nonsingular intersections with the Hessian.

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 79, 95-98, and 151-161, 1959.