2016/01/18 by Rodrigo Gondim, Gondim, Rodrigo, Giuseppe Zappalà +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1601.04454
openalex publication_date 2016/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a family of standard bigraded binomial Artinian Gorenstein\nalgebras, whose combinatoric structure characterizes the ones presented by\nquadrics. These algebras provide, for all socle degree grater than two and in\nsufficiently large codimension with respect to the socle degree,\ncounter-examples to Migliore-Nagel conjectures, see citeMN1 and citeMN2.\nOne of them predicted that Artinian Gorenstein algebras presented by quadratics\nshould satisfy the weak Lefschetz property. We also prove a generalization of a\nHessian criterion for the Lefschetz properties given by Watanabe, see\n citeWa1 and citeMW, which is our main tool to control the Weak Lefschetz\nproperty.\n