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arXiv · 2307.14483

A criterion for sequential Cohen-Macaulayness

Giulio Caviglia·Alessandro De Stefani
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Abstract

The purpose of this note is to show that a finitely generated graded module $M$ over $S=k[x_1,\ldots,x_n]$, $k$ a field, is sequentially Cohen-Macaulay if and only if its arithmetic degree ${\rm adeg}(M)$ agrees with ${\rm adeg}(F/{\rm gin}_{revlex}(U))$, where $F$ is a graded free $S$-module and $M \cong F/U$. This answers positively a conjecture of Lu and Yu from 2016.

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Giulio Caviglia, Alessandro De Stefani. 2023-07-26. A criterion for sequential Cohen-Macaulayness. https://arxiv.org/abs/2307.14483

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