The weak Lefschetz property for quotients by quadratic monomials

• Juan Migliore ^[3] ; Uwe Nagel ^[1] ; Hal Schenck ^[2]
  1. [1] University of Kentucky

     University of Kentucky

     Estados Unidos

     
  2. [2] Iowa State University

     Iowa State University

     Township of Franklin, Estados Unidos

     
  3. [3] University of Notre Dame (Estados Unidos)

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• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 126, Nº 1, 2020, págs. 41-60
• Idioma: inglés
• DOI: 10.7146/math.scand.a-116681
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.