Eigenvalues of rank one perturbations of unstructured matrices

Let A be a fixed complex matrix and let $u\text{,}v$ be two vectors. The eigenvalues of matrices $A+\tau {\mathit{uv}}^{?}$ $(\tau \in \mathbb{R})$ form a system of intersecting curves. The dependence of the intersections on the vectors $u\text{,}v$ is studied.