Alexandra Seceleanu: Artinian Gorenstein algebras having binomial Macaulay dual generator

Abstract.

Every graded artinian Gorenstein ring corresponds via Macaulay-Matlis duality to a homogeneous polynomial, called a Macaulay dual generator. In this way, Macaulay dual generators which are monomials correspond to monomial complete intersection rings. Monomial complete intersections have particularly nice properties: their natural generators form a Gröbner basis, their minimal free resolutions are well understood, and they satisfy the strong Lefschetz property (in characteristic zero).

In this talk we consider Macaulay dual generators which are the difference of two monomials and we seek to understand to what extent the properties listed above still persist for the corresponding artinian Gorenstein algebras. This is joint work with Nasrin Altafi, Rodica Dinu, Sara Faridi, Shreedevi K. Masuti, Rosa M. Miró-Roig, and Nelly Villamizar.