Gorenstein algebras from simplicial complexes

Abstract: Gorenstein algebras form an intriguing class of objects which often show up in combinatorics and geometry. In this talk I will present a construction which associates to every pure simplicial complex a standard graded Gorenstein algebra. We describe a presentation of this algebra as a polynomial ring modulo an ideal generated by monomials and pure binomials. When the simplicial complex is flag, i.e., it is the clique complex of its graph, our main results establish equivalences between well studied properties of the complex (being S_2, Cohen-Macaulay, Shellable) with those of the algebra (being quadratic, Koszul, having a quadratic GB). Finally, we study the h-vector of the Gorenstein algebras in our construction and answer a question of Peeva and Stillman by showing that it is very often not gamma-positive. This is joint work with Alessio D'Alì.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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