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arXiv · 1912.10864

On the initial Betti numbers

Mohsen Asgharzadeh
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Abstract

Let $R$ 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 $β_0(ω_{\frac{R}{I}})$ in some cases, where $I$ is a product of two ideals.

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Mohsen Asgharzadeh. 2026-01-28. On the initial Betti numbers. https://arxiv.org/abs/1912.10864

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