English

The Weak Lefschetz property for quotients by Quadratic Monomials

Commutative Algebra 2017-06-19 v1

Abstract

In [MMR], Micha\l{}ek--Mir\'o-Roig give a beautiful geometric characterization of Artinian quotients by ideals generated by quadratic or cubic monomials, such that the multiplication map by a general linear form fails to be injective in the first nontrivial degree. Their work was motivated by conjectures of Ilardi and Mezzetti-Mir\'o-Roig-Ottaviani, connecting the failure to Laplace equations and classical results of Togliatti on osculating planes. We study quotients by quadratic monomial ideals, explaining failure of the Weak Lefschetz Property for some cases not covered by [MMR].

Keywords

Cite

@article{arxiv.1706.05058,
  title  = {The Weak Lefschetz property for quotients by Quadratic Monomials},
  author = {Juan Migliore and Uwe Nagel and Hal Schenck},
  journal= {arXiv preprint arXiv:1706.05058},
  year   = {2017}
}

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15 pages