Singular hypersurfaces characterizing the Lefschetz properties

@article{Gennaro2014SingularHC,
  title={Singular hypersurfaces characterizing the Lefschetz properties},
  author={Roberta Di Gennaro and Giovanna Ilardi and Jean Vall{\`e}s},
  journal={J. London Math. Society},
  year={2014},
  volume={89},
  pages={194-212}
}
In a recent paper [17] Miro-Roig, Mezzetti and Ottaviani highlight the link between rational varieties satisfying a Laplace equation and artinian ideals failing the Weak Lefschetz Property. Continuing their work we extend this 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). This characterization allows us to solve three… CONTINUE READING

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