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arXiv · 2404.07297

Betti cones over fibre products

H. Ananthnarayan·Omkar Javadekar·Rajiv Kumar
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Abstract

Let $R$ be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded $R$-modules. As an application of this, we show that the existence of an $R$-module of finite regularity and infinite projective dimension forces $R$ to be Koszul. We also look at the extremal rays of the Betti cone of finitely generated graded $R$-modules, and show that when $\operatorname{depth}(R)=1$, they are spanned by the Betti tables of pure $R$-modules if and only if $R$ is Cohen-Macaulay with minimal multiplicity.

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H. Ananthnarayan, Omkar Javadekar, Rajiv Kumar. 2024-04-10. Betti cones over fibre products. https://arxiv.org/abs/2404.07297

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