随机单项理想合冲的特征依赖性
交换代数
2021-01-08 v3 代数几何
组合数学
摘要
合冲何时依赖于域的特征？即便对深入研究过的例子族，也知之甚少。对于一类随机单项理想，即随机旗复形的Stanley–Reisner理想，我们证明了Betti数在渐近意义上几乎总是依赖于特征。利用该结果，我们还发展了代数簇渐近合冲特征依赖性的一种启发式方法。
引用
@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}
}
备注
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