Invariants of curves in $RP^2$ and $R^2$

Abstract

There is an elegant relation found by Fabricius-Bjerre [Math. Scand 40 (1977) 20–24] among the double tangent lines, crossings, inflections points, and cusps of a singular curve in the plane. We give a new generalization to singular curves in $R{P}^2$. We note that the quantities in the formula are naturally dual to each other in $R{P}^2$, and we give a new dual formula.