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Singular hypersurfaces characterizing the Lefschetz properties Valles, Jean


In a recent paper, Mezzetti, Miro-Roig and Ottaviani [Mezzetti et al., “Laplace equations and the weak Lefschetz property”, Canad. J. Math. 65 (2013) 634654] highlight the link between rational varieties satisfying a Laplace equation and artinian ideals failing the Weak Lefschetz Property. In a joint work with Roberta di Gennaro and Giovanna Ilardi [“Singular hypersurfaces characterizing the Lefschetz properties”, J. London Math. Soc. (2014) 89 (1):194-212] we extended their link to the more general situation of artinian ideals failing the Strong Lefschetz Property. We characterize the failure of the SLP (which includes WLP) by the existence of special singular hypersurfaces (cones for WLP). Thank to this characterization we relate, for instance, the splitting type of derivation bundles associated to a line arrangements to the failure of the SLP of some artinians ideals

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