Star configuration points and generic plane curves Academic Article uri icon

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abstract

  • Let 1 , , l \ell _1,\ldots ,\ell _l be l l lines in P 2 \mathbb {P}^2 such that no three lines meet in a point. Let X ( l ) \mathbb {X}(l) be the set of points { i j   |   1 i > j l } P 2 \{\ell _i \cap \ell _j ~|~ 1 \leq i > j \leq l\} \subseteq \mathbb {P}^2 . We call X ( l ) \mathbb {X}(l) a star configuration. We describe all pairs ( d , l ) (d,l) such that the generic degree d d curve in P 2 \mathbb {P}^2 contains an X ( l ) \mathbb {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.

publication date

  • December 1, 2011