Van Duc Trung

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math.AC2025

On the Stability of Bass and Betti Numbers under Ideal Perturbations in a Local Ring

Van Duc Trung

Let $(R, m)$ be a Noetherian local ring, and let $J$ be an arbitrary ideal of $R$ . Suppose $M$ is a finitely generated $R$ -module. Let $x_{1}, \dots, x_{r}$ be a $J$ -filter re…

math.AC2025

Koszul Homology Under Small Perturbations

Van Duc Trung

Let $x_{1}, \dots, x_{s}$ be a filter regular sequence in a local ring $(R, m)$ . Denote by $R_{x_{1}, \dots, x_{s}}$ the Koszul complex of $x_{1}, \dots, x_{s}$ over $R$ . In this paper,…

math.AC2025

The second Hilbert coefficient of modules with almost maximal depth

Van Duc Trung

Let $M = {M_{n}}$ be a good $q$ -filtration of a finitely generated $R$ -module $M$ of dimension $d$ , where $(R, m)$ is a local ring and $\mathfrak{q}…