3 papers
math.AC2024
Stanley-Reisner Ideals with Pure Resolutions
David Carey, Mordechai Katzman
This paper investgates Stanley-Reisner ideals with pure resolutions. We first describe two infinite families of such ideals associated to highly symmetric complexes. We then prove…
math.AC2024
Betti Cones of Stanley-Reisner Ideals
David Carey
The aim of this thesis is to investigate the Betti diagrams of squarefree monomial ideals in polynomial rings. We use two key tools to help us study these diagrams. The first is th…
math.AC2021
Dimensions of Betti Cones on Edge Ideals
David Carey
Boij-Söderberg Theory views the Betti diagrams of graded modules over polynomial rings as vectors in a rational vector space, and studies the cone that these vectors generate (call…