Lefschetz properties for Artinian Gorenstein algebras presented by quadrics

Autor:	Gondim, Rodrigo, Zappalà, Giuseppe
Rok vydání:	2016
Předmět:	Mathematics - Commutative Algebra Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	We introduce a family of standard bigraded binomial Artinian Gorenstein algebras, whose combinatoric structure characterizes the ones presented by quadrics. These algebras provide, for all socle degree grater than two and in sufficiently large codimension with respect to the socle degree, counter-examples to Migliore-Nagel conjectures, see \cite{MN1} and \cite{MN2}. One of them predicted that Artinian Gorenstein algebras presented by quadratics should satisfy the weak Lefschetz property. We also prove a generalization of a Hessian criterion for the Lefschetz properties given by Watanabe, see \cite{Wa1} and \cite{MW}, which is our main tool to control the Weak Lefschetz property. Comment: Comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1601.04454 Zobrazit plný text záznamu View this record from Arxiv