Resumen
We present three main results. The first two provide sufficient conditions in order that a planar polynomial vector field in C2 has a rational first integral, and the third one studies the number of multiple points that an invariant algebraic curve of degree n of a planar polynomial vector field of degree m can have in function of m and n.

Resumen
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system , , inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles.