Nicolae Vulpe
Moldova State University, Vladimir Andrunachievici Institute of Mathematics and Computer Science, Chişinău, Moldova

We consider the family ${\bf QSL}_{\bf 3}$ of quadratic differential systems possessing invariant straight lines, finite and infinite, of total multiplicity exactly three. In a sequence of papers, the complete study of quadratic systems with invariant lines of total multiplicity at least four was achieved. In addition, some subfamilies of quadratic systems possessing invariant lines of total multiplicity at least three were also studied, among them the Lotka-Volterra family. However, there were still systems in ${\bf QSL}_{\bf 3}$ that remain to be studied. So we complete the study of the geometric configurations of invariant lines of ${\bf QSL}_{\bf 3}$ by studying all the remaining cases and give the full classification of this family modulo their configurations of invariant lines. This classification is done in affine invariant terms and we present here the "bifurcation" diagram of the configurations in the 12-parameter space of coefficients of the systems. This diagram provides an algorithm for deciding for any given system whether it belongs to ${\bf QSL}_{\bf 3}$ and in case it does, by producing its configuration of invariant straight lines.