3 papers
math.AC2020
Asymptotic Degree of Random Monomial Ideals
Lily Silverstein, Dane Wilburne, Jay Yang
One of the fundamental invariants connecting algebra and geometry is the degree of an ideal. In this paper we derive the probabilistic behavior of degree with respect to the versat…
math.AC2020
Characteristic dependence of syzygies of random monomial ideals
Caitlyn Booms, Daniel Erman, Jay Yang
When do syzygies depend on the characteristic of the field? Even for well-studied families of examples, very little is known. For a family of random monomial ideals, namely the Sta…
math.AC2019
Virtual Resolutions of Monomial Ideals on Toric Varieties
Jay Yang
We use cellular resolutions of monomial ideals to prove an analog of Hilbert's syzygy theorem for virtual resolutions of monomial ideals on smooth toric varieties.