Van Duc Trung

activity

20182026

most citedThe initial ideal of generic sequences and Fröberg's Conjecture

4 citations · 4 across the 4 of their papers we have counts for

collaborators

6 papers

math.AC2026

When Hilbert functions determine four-variable generic initial ideals

Van Duc Trung

Over a field of characteristic zero, we characterize the Hilbert functions that determine the degree reverse lexicographic generic initial ideal among Artinian quotients in four va…

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}…

math.AC2020

Small perturbations in generalized Cohen-Macaulay local rings

Pham Hung Quy, Van Duc Trung

Let $(R, m)$ be a generalized Cohen-Macaulay local ring of dimension $d$ , and $f_{1}, \dots, f_{r}$ a part of system of parameters of $R$ . In this paper we give explicit numbers…

math.AC2018★ 4 cited

The initial ideal of generic sequences and Fröberg's Conjecture

Van Duc Trung

Let $K$ be an infinite field and let $I = (f_{1}, \dots, f_{r})$ be an ideal in the polynomial ring $R = K [x_{1}, \dots, x_{n}]$ generated by generic forms of degrees $d_{1}, \dots, d_{r}$ . A lon…