Characteristic dependence of syzygies of random monomial ideals
Abstract
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 Stanley--Reisner ideals of random flag complexes, we prove that the Betti numbers asymptotically almost always depend on the characteristic. Using this result, we also develop a heuristic for characteristic dependence of asymptotic syzygies of algebraic varieties.
Keywords
Cite
@article{arxiv.2007.13914,
title = {Characteristic dependence of syzygies of random monomial ideals},
author = {Caitlyn Booms and Daniel Erman and Jay Yang},
journal= {arXiv preprint arXiv:2007.13914},
year = {2021}
}
Comments
We have reworked the title, abstract, and introduction to reflect the paper's primary focus on homological behavior of random flag complexes. Further, Section 1.1 was added, which tries to more clearly explain how questions about asymptotic syzygies provided motivation for this work and how we see our new results as providing motivation for new conjectures about syzygies in geometric settings