STAR CONFIGURATION POINTS AND GENERIC PLANE CURVES.

Let l1, … , ll be l lines in P² such that no three lines meet in a point. Let X(l) be the set of points {li ∩lj ∣ 1 ≤ i < j ≤ l} ⊆ P². We call X(l) a star configuration. We describe all pairs (d, l) such that the generic degree d curve in P² contains an X(l). Our proof strategy uses both a theoretical and an explicit algorithmic approach. We also describe how one may extend our algorithmic approach to similar problems. [ABSTRACT FROM AUTHOR]