Archivio Istituzionale della RicercaLet 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.
Star configuration points and generic plane curves / Carlini, E.; van Tuyl, A.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 139:12(2011), pp. 4181-4192. [10.1090/S0002-9939-2011-11204-8]
Star configuration points and generic plane curves
Carlini E.;
2011
Abstract
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.
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https://hdl.handle.net/11583/2875952