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Lefschetz properties for Artinian Gorenstein algebras presented by quadrics


Authors: Rodrigo Gondim and Giuseppe Zappalà
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 13A02, 05E40; Secondary 13D40, 13E10
DOI: https://doi.org/10.1090/proc/13822
Published electronically: October 30, 2017
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Abstract: We introduce a family of Artinian Gorenstein algebras, whose combinatorial structure characterizes the ones presented by quadrics. Under certain hypotheses these algebras have non-unimodal Hilbert vector. In particular we provide families of counterexamples to the conjecture that Artinian Gorenstein algebras presented by quadrics should satisfy the weak Lefschetz property.


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Rodrigo Gondim
Affiliation: Universidade Federal Rural de Pernambuco, av. Don Manoel de Medeiros s/n, Dois Irmos - Recife - PE 52171-900, Brazil
Email: rodrigo.gondim@ufrpe.br

Giuseppe Zappalà
Affiliation: Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 5, 95125 Catania, Italy
Email: zappalag@dmi.unict.it

DOI: https://doi.org/10.1090/proc/13822
Received by editor(s): December 19, 2016
Received by editor(s) in revised form: April 27, 2017
Published electronically: October 30, 2017
Additional Notes: The first author was partially supported by the CAPES postdoctoral fellowship, Proc. BEX 2036/14-2
The second author was part of the Research Project of the University of Catania FIR 2014 “Aspetti geometrici e algebrici della Weak e Strong Lefschetz Property”
Communicated by: Irena Peeva
Article copyright: © Copyright 2017 American Mathematical Society