In this article we consider the action of affine group and time rescaling onplanar quadratic differential systems. We construct a system of representativesof the orbits of systems with four invariant lines, including the line atinfinity and including multiplicities. For each orbit we exhibit itsconfiguration. We characterize in terms of algebraic invariants and comitantsand also geometrically, using divisors of the complex projective plane, theclass of quadratic differential systems with four invariant lines. Theseconditions are such that no matter how a system may be presented, one canverify by using them whether the system has exactly four invariant linesincluding multiplicities, and if it is so, to check to which orbit (or familyof orbits) it belongs.
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