THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN Pn AND THE WEAK LEFSCHETZ PROPERTY
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We find the Hilbert function and the minimal free resolution of a star-configuration in Pn. The conditions are provided under which the Hilbert function of a star-configuration in P2 is generic or non-generic. We also prove that if X and Y are linear star-configurations in P2 of types t and s, respectively, with s ≥ t ≥3, then the Artinian k-algebra R=(IX + IY) has the weak Lefschetz property.
Abstract
We find the Hilbert function and the minimal free resolution of a star-configuration in Pn. The conditions are provided under which the Hilbert function of a star-configuration in P2 is generic or non-generic. We also prove that if X and Y are linear star-configurations in P2 of types t and s, respectively, with s ≥ t ≥3, then the Artinian k-algebra R=(IX + IY) has the weak Lefschetz property.
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