Lefschetz properties in algebra and geometry

• Martí Salat Moltó ^[1]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
• Localización: Reports@SCM: an electronic journal of the Societat Catalana de Matemàtiques, ISSN-e 2385-4227, Vol. 4, Nº. 1, 2018, págs. 21-29
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen
  • català

    La propietat dèbil de Lefschetz (WLP) té un paper important tant a l’`algebra com a la geometria. A [3], Mezzetti, Miró-Roig i Ottaviani van demostrar que el fet que certs ideals Artinians deK[x0, ... ,xn] fallin la WLP té relació ambl’existència de projeccions de la varietat de Veronese que satisfan una equació de Laplace. Aquest vincle dóna lloc a la definició de sistema de Togliatti. En aquest article, enunciarem alguns resultats recents obtinguts sobre el tema. En particular exposem la classificació dels sistemes de Togliatti minimals i llisos generats per2n+ 3 monomis de graud≥10 obtinguts a [8].

  • English

    The weak Lefschetz property (WLP) plays an important role both in algebra and geometry. In [3], Mezzetti, Miró-Roig and Ottaviani found that the failure of the WLP for some particular Artinian ideals in K[x0, ... , xn] is related with the existence of projections of the Veronese variety satisfying one Laplace equation. This relation gives rise to the denition of Togliatti system. In this note, we state some recent results on this topic. In particular, we expose the classication of minimal smooth Togliatti systems generated by 2n +3 monomials of degree d ≥ 10 obtained in [8].Keywords: weak Lefschetz property, Togliatti systems, Laplace equations.

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