English

On the initial Betti numbers

Commutative Algebra 2026-01-29 v2

Abstract

Let RR be a Cohen-Macaulay local ring possessing a canonical module. We compare the initial and terminal Betti numbers of modules in a series of nontrivial cases. We pay special attention to the Betti numbers of the canonical module. Also, we compute β0(ωRI)\beta_0(\omega_{\frac{R}{I}}) in some cases, where II is a product of two ideals.

Keywords

Cite

@article{arxiv.1912.10864,
  title  = {On the initial Betti numbers},
  author = {Mohsen Asgharzadeh},
  journal= {arXiv preprint arXiv:1912.10864},
  year   = {2026}
}
R2 v1 2026-06-23T12:54:40.069Z