In this work we use the algebro-geometric concept of divisor on a projective curve in the study of planar quadratic vector fields. We introduce here specific divisors to encode global information about the geometry at infinity of quadratic systems with a weak focus which is not a center and we show that these concepts organise and unify in an intrinsic way this information. This geometric approach forms a link between chart-dependent classification studies of quadratic (or cubic) differential systems and affine-invariant results based on the algebraic theory of invariants of differential systems.