  We give some real polynomials in two variables of degrees 4, 5, and 6 whose
hessian curves have more connected components than had been known previously.
In particular, we give a quartic polynomial whose hessian curve has 4 compact
connected components (ovals), a quintic whose hessian curve has 8 ovals, and a
sextic whose hessian curve has 11 ovals.
