4 papers
Asymptotic properties of random monomial ideals
Fatemeh Mohammadi, Sonja PetroviÄ, Eduardo Sáenz-de-Cabezón
This paper focuses on asymptotic properties of random monomial ideals through a statistical viewpoint. It extends the study of redundancy in monomial ideals by analyzing the poset…
Minimal cellular resolutions of powers of matching field ideals
Oliver Clarke, Fatemeh Mohammadi
We study a family of monomial ideals, called block diagonal matching field ideals, which arise as monomial Gröbner degenerations of determinantal ideals. Our focus is on the minim…
A Family of Monomial Gröbner Degenerations of Determinantal Ideals with Minimal Cellular Resolutions
Fatemeh Mohammadi
We explore a family of monomial ideals derived as Gröbner degenerations of determinantal ideals. These ideals, previously examined as block diagonal matching field ideals within t…
Liftable Point-Line Configurations: Defining Equations and Irreducibility of Associated Matroid and Circuit Varieties
Oliver Clarke, Giacomo Masiero, Fatemeh Mohammadi
We study point-line configurations through the lens of projective geometry and matroid theory. Our focus is on their realisation spaces, where we introduce the concepts of liftable…