14 citations · 58 across the 19 of their papers we have counts for
20 papers · 1 filter
Saturation degree of powers of graded ideals
Le Tuan Hoa, Hop Dang Nguyen, Ngo Viet Trung
Let be a non-nilpotent graded ideal of a standard graded algebra over a Noetherian commutative ring. We show that the saturation degree sdeg is asymptotically a constant…
New bounds on Castelnuovo--Mumford regularity of monomial curves and application to sumsets
Le Tuan Hoa, Doan Quang Tien
A monomial curve is defined by a sequence of coprime integers . One gap of this sequence is . Gruson--Lazarsfeld--Peskine…
Regularity functions of powers of graded ideals
Le Tuan Hoa, Hop Dang Nguyen, Ngo Viet Trung
This paper studies the problem of which sequences of non-negative integers arise as the functions , , $\operatorname{reg}…
Upper bounds on two Hilbert coefficients
Le Xuan Dung, Juan Elias, Le Tuan Hoa
New upper bounds on the first and the second Hilbert coefficients of a Cohen-Macaulay module over a local ring are given. Characterizations are provided for some upper bounds to be…
Maximal generating degrees of powers of homogeneous ideals
Le Tuan Hoa
The degree excess function is the difference between the maximal generating degree of a homogeneous ideal of a polynomial ring and , where is th…
Asymptotic behavior of Integer Programming and the stability of the Castelnuovo-Mumford regularity
Le Tuan Hoa
The paper provides a connection between Commutative Algebra and Integer Programming and contains two parts. The first one is devoted to the asymptotic behavior of integer programs…
Powers of Monomial Ideals and Combinatorics
Le Tuan Hoa
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative…
A note on Castelnuovo-Mumford regularity and Hilbert coefficients
Le Xuan Dung, Le Tuan Hoa
New upper and lower bounds on the Castelnuovo-Mumford regularity are given in terms of the Hilbert coefficients. Examples are provided to show that these bounds are in some sense n…
Dependence of Hilbert coefficients
Le Xuan Dung, Le Tuan Hoa
Let be a finitely generated module of dimension and depth over a Noetherian local ring () and an -primary ideal. In the main result…
Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals
Le Tuan Hoa, Tran Nam Trung
Let be a monomial ideal in a polynomial ring . In this paper we give an upper bound on $\overline{\dstab} (I)$ in terms of and the maximal generatin…
Castelnuovo-Mumford regularity of associated graded modules and fiber cones of filtered modules
Le Xuan Dung, Le Tuan Hoa
We give bounds on the Castelnuovo-Mumford regularity of the associated graded module of an arbitrary good filtration and of its fiber cone. These bounds extend previous results of…
On local cohomology of a tetrahedral curve
Do Hoang Giang, Le Tuan Hoa
It is shown that the diameter $\diam (H^1_\mfr(R/I))$ of the first local cohomology module of a tetrahedral curve can be explicitly expressed in terms of the $a…
Gröbner bases of simplicial toric ideals
M. Hellus, J. Stueckrad, L. T. Hoa
Bounds for the maximum degree of a minimal Gröbner basis of simplicial toric ideals with respect to the reverse lexicographic order are given. These bounds are close to the bound s…
Castelnuovo-Mumford regularity of Ext modules and homological degree
Marc Chardin, Dao Thanh Ha, Le Tuan Hoa
Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and n…
Gröbner bases of simplicial toric ideals
M. Hellus, J. Stueckrad, L. T. Hoa
Bounds for the maximal degree of certain Gröbner bases of simplicial toric ideals are given. These bounds are close to the bound stated in Eisenbud-Goto's Conjecture on the Casteln…
Castelnuovo-Mumford regularity and reduction number of smooth monomial curves
Michael Hellus, Lê Tuân Hoa, Jürgen Stückrad
We compare, for smooth monomial projective curves, the Castel- nuovo-Mumford regularity and the reduction number; we present an example where these two numbers differ. However, we…
Stability of associated primes of monomial ideals
Lê Tuân Hoa
Let be a monomial ideal of a polynomial ring . In this paper we determine a number such that $\Ass (I^n/I^{n+1}) = \Ass (I^{B}/I^{B+1})$ for all .
Castelnuovo-Mumford regularity of canonical and deficiency modules
Lê Tuân Hoa, Eero Hyry
We give two kinds of bounds for the Castelnuovo-Mumford regularity of the canonical module and the deficiency modules of a ring, respectively in terms of the homological degree and…
Borel-fixed ideals and reduction number
Le Tuan Hoa, Ngo Viet Trung
The aim of this paper is to study the relationship between reduction numbers and Borel-fixed ideals in all characteristics. By definition, Borel-fixed ideals are closed under certa…
Asymptotic linear bounds for the Castelnuovo-Mumford regularity
Juergen Herzog, Le Tuan Hoa, Ngo Viet Trung
We prove asymptotic linear bounds for the Castelnuovo-Mumford regularity of certain filtrations of homogeneous ideals whose Rees algebras need not to be Noetherian.