Trung Chau

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math.AC2025

The $F$ -singularities of algebras defined by permanents

Trung Chau

Let $X$ be a matrix of indeterminates, $t$ an integer, and $P_{t} (X)$ define the ideal generated by the permanents of all $t \times t$ submatrix of $X$ . $P_{t} (X)$ is called a permanent…

math.AC2025

Maximal minors of $1$ -generic matrices have rational singularities

Trung Chau, Manoj Kummini

We show that the quotient ring by the ideal of maximal minors of a $1$ -generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are n…

math.AC2025

Permanental ideals of symmetric matrices

Trung Chau

In this article, we study the ideal generated by $2 \times 2$ permanents of a symmetric matrix. We denote this ideal by $P_{2} (X)$ where $X$ is a symmetric matrix. We compute a Gröbne…

math.AC2025

Admissible matchings and the Castelnuovo-Mumford regularity of square-free powers

Trung Chau, Kanoy Kumar Das, Amit Roy +1

Let $I$ be any square-free monomial ideal, and $H_{I}$ denote the hypergraph associated with $I$ . Refining the concept of $k$ -admissible matching of a graph defined by Erey…

math.AC2025

Homological invariants of edge ideals of weighted oriented graphs

Trung Chau, Richie Sheng, Deborah Wooton

We determine all possible triples of depth, dimension, and regularity of edge ideals of weighted oriented graphs with a fixed number of vertices. Also, we compute all the possible…

The F-singularities of algebras defined by permanents

Maximal minors of 1-generic matrices have rational singularities

Permanental ideals of symmetric matrices

Admissible matchings and the Castelnuovo-Mumford regularity of square-free powers

Homological invariants of edge ideals of weighted oriented graphs

The $F$ -singularities of algebras defined by permanents

Maximal minors of $1$ -generic matrices have rational singularities