The weak lefschetz property for quotients by quadratic monomials

Juan Migliore; Uwe Nagel; Hal Schenck

doi:10.7146/math.scand.a-116681

The weak lefschetz property for quotients by quadratic monomials

Juan Migliore, Uwe Nagel, Hal Schenck

Mathematics

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9 Scopus citations

Abstract

Michałek and Miró-Roig, in J. Combin. Theory Ser. A 143 (2016), 66-87, 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, Miró-Roig and 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 Michałek and Miró-Roig.

Original language	English
Pages (from-to)	41-60
Number of pages	20
Journal	Mathematica Scandinavica
Volume	126
Issue number	1
DOIs	https://doi.org/10.7146/math.scand.a-116681
State	Published - 2020

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ASJC Scopus subject areas

General Mathematics

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The weak lefschetz property for quotients by quadratic monomials

Abstract

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