Ye's conjecture on invariant lines of planar polynomial systems

Let $P_n(x,y)$ and $Q_n(x,y)$ be polynomials of degree $n$, defining the planar polynomial system

$$\dot{x}=P_n(x,y),\qquad \dot{y}=Q_n(x,y).$$

An invariant line is a straight line preserved by the flow of this system. Ye's conjecture. When $n$ is odd, the system has at most $M_n=2n+2$ invariant lines; when $n$ is even, it has at most $M_n=2n+1$ invariant straight lines. The conjecture concerns upper bounds for invariant straight lines in planar polynomial systems and is false for $n>4$.