TY - JOUR AU - Migliore, Juan AU - Nagel, Uwe AU - Schenck, Hal PY - 2020/03/29 Y2 - 2024/03/29 TI - The weak Lefschetz property for quotients by quadratic monomials JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 126 IS - 1 SE - Articles DO - 10.7146/math.scand.a-116681 UR - https://www.mscand.dk/article/view/116681 SP - 41-60 AB - <p>Michałek and Miró-Roig, in J. Combin. Theory Ser.&nbsp;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&nbsp;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&nbsp;Miró-Roig.</p> ER -