Star configuration points and generic plane curves

Let ℓ1,...,ℓ1 be l lines in ℙ2 such that no three lines meet in a point. Let X(l) be the set of points {ℓi ∩ ℓj {divides} 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. © 2011 American Mathematical Society