arXiv subjects

Thái Thành Nguyên

Publications and source records attributed to Thái Thành Nguyên.

5 recordsLinked to original sources

arXiv2022

Chudnovsky's Conjecture and the stable Harbourne-Huneke containment for general points

In our previous work with Grifo and Hà, we showed the stable Harbourne-Huneke containment and Chudnovsky's conjecture for the defining ideal of sufficiently many general points in $\mathbb{P}^N$. In this paper, we establish the conjectures for all remaining cases, and hence, give the affirmative answer to Harbourne-Huneke containment and Chudnovsky's conjecture for any number of general points in $\mathbb{P}^N$ for all $N$. Our new technique is to develop the Cremona reduction process that provides effective lower bounds for the Waldschmidt constant of the defining ideals of generic points in projective spaces.

math.AC↗

arXiv2022

The Initial Degree of Symbolic Powers of Fermat-like Ideals of Planes and Lines Arrangements

We explicitly compute the least degree of generators of all symbolic powers of the defining ideal of Fermat-like configuration of lines in $\mathbb{P}^3_\mathbb{C}$, except for the second symbolic powers, where we provide bounds for them. We will also explicitly compute those numbers for ideal determining the singular locus of the arrangement of lines given by the pseudoreflection group $A_3$. As direct applications, we verify Chudnovsky's(-like) Conjecture, Demailly's(-like) Conjecture and Harbourne-Huneke Containment problem as well as calculate the Waldschmidt constant and (asymptotic) resurgence number.

math.AC↗

arXiv2021

RandomPoints package for Macaulay2

We present {\tt RandomPoints}, a package in \emph{Macaulay2} designed mainly to identify rational and geometric points in a variety over a finite field. We provide tools to estimate the dimension of a variety. We also present methods to obtain non-vanishing minors of a given size in a given matrix, by evaluating the matrix at a point.

math.AG↗

arXiv2021

Chudnovsky's Conjecture and the stable Harbourne-Huneke containment

In this paper, we investigate containment statements between symbolic and ordinary powers and bounds on the Waldschmidt constant of defining ideals of points in projective spaces. We establish the stable Harbourne conjecture for the defining ideal of a general set of points. We also prove Chudnovsky's Conjecture and the stable version of the Harbourne--Huneke containment conjectures for a general set of sufficiently many points.

math.AC↗

arXiv2021

Demailly's Conjecture and the Containment Problem

We investigate Demailly's Conjecture for a general set of sufficiently many points. Demailly's Conjecture generalizes Chudnovsky's Conjecture in providing a lower bound for the Waldschmidt constant of a set of points in projective spaces. We also study a containment between symbolic and ordinary powers conjectured by Harbourne and Huneke that in particular implies Demailly's bound, and prove that a general version of that containment holds for generic determinantal ideals and defining ideals of star configurations.

math.AC↗