Hyperplane sections and the subtlety of the Lefschetz properties

Details Hyperplane sections and the subtlety of the Lefschetz properties Hyperplane sections and the subtlety of the Lefschetz properties

2010-12-12

arxiv.org/abs/1012.2601v1

J. Pure Appl. Algebra 216 (2012), no. 1, 108-114

Mathematics

Commutative Algebra

9 pages

Scientific paper

10.1016/j.jpaa.2011.05.007

The weak and strong Lefschetz properties are two basic properties that Artinian algebras may have. Both Lefschetz properties may vary under small perturbations or changes of the characteristic. We study these subtleties by proposing a systematic way of deforming a monomial ideal failing the weak Lefschetz property to an ideal with the same Hilbert function and the weak Lefschetz property. In particular, we lift a family of Artinian monomial ideals to finite level sets of points in projective space with the property that a general hyperplane section has the weak Lefschetz property in almost all characteristics, whereas a special hyperplane section does not have this property in any characteristic.

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