5 papers
Constructing Koszul filtrations: existence and non-existence for G-quadratic algebras
Emily Berghofer, Lisa Nicklasson, Peder Thompson +1
Given a standard graded algebra over a field, we consider the relationship between G-quadraticity and the existence of a Koszul filtration. We show that having a quadratic Gröbner…
Spheres and balls as independence complexes
Susan M. Cooper, Sara Faridi, Thiago Holleben +2
The terms "whiskering", and more generally "grafting", refer to adding generators to any monomial ideal to make the resulting ideal Cohen-Macaulay. We investigate the independence…
Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property
Thiago Holleben, Lisa Nicklasson
Inspired by the Roller Coaster Theorem from graph theory, we prove the existence of artinian Gorenstein algebras with unconstrained Hilbert series, which we call Roller Coaster alg…
Subalgebras generated in degree two with minimal Hilbert function
Lisa Nicklasson
What can be said about the subalgebras of the polynomial ring, with minimal or maximal Hilbert function? This question was discussed in a recent paper by M. Boij and A. Conca. In t…
On generic principal ideals in the exterior algebra
Samuel Lundqvist, Lisa Nicklasson
We give a lower bound on the Hilbert series of the exterior algebra modulo a principal ideal generated by a generic form of odd degree and disprove a conjecture by Moreno-Socías an…