Lefschetz properties in algebra and geometry Autors/ores Martí Salat Moltó Universitat de Barcelona Paraules clau: weak Lefschetz property, Togliatti systems, Laplace equations. Resum The weak Lefschetz property (WLP) plays an important role both in algebra and geometry. In , 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 .Keywords: weak Lefschetz property, Togliatti systems, Laplace equations. Descàrregues PDF (English) Com citar Salat Moltó, M. (2019). Lefschetz properties in algebra and geometry. Reports@SCM, 4(1), 21–29. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/145799 Més formats de citació ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Descarregar citació Endnote/Zotero/Mendeley (RIS) BibTeX Número Vol. 4 Núm. 1 (2018) Secció Articles Llicència The intellectual property of articles belongs to the respective authors.On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.