Vertex cover algebras of unimodular hypergraphs (2007)
Herzog, Jurgen, Hibi, Takayuki, Trung, Ngo Viet
It is proved that all vertex cover algebras of a hypergraph are standard graded if and only if the hypergraph is unimodular. This has interesting consequences on the symbolic powers of monomial...
On the regularity of products and intersections of complete intersections (2007)
Chardin, Marc, Minh, Nguyen Cong, Trung, Ngo Viet
This paper proves that the Castelnuovo-Mumford regularities of the product and sum of two monomial complete intersection ideals are at most the sum of the regularities of the two ideals, and provides...
Integral closures of monomial ideals and Fulkersonian hypergraphs (2006)
We prove that the integral closures of the powers of a squarefree monomial ideal I equal the symbolic powers if and only if I is the edge ideal of a Fulkersonian hypergraph.
Uniform bounds in generalized Cohen-Macaulay rings (2006)
Linh, Cao Huy, Trung, Ngo Viet
We establish a uniform bound for the Castelnuovo-Mumford regularity of associated graded rings of parameter ideals in a generalized Cohen-Macaulay ring. As consequences, we obtain uniform bounds for...
Herzog, Juergen, Hibi, Takayuki, Murai, Satoshi, Trung, Ngo Viet, Zheng, Xinxian
A forest is the clique complex of a strongly chordal graph and a quasi-forest is the clique complex of a chordal graph. Kruskal--Katona type theorems for forests, quasi-forests, pure forests and pure...
Standard graded vertex cover algebras, cycles and leaves (2006)
Herzog, Juergen, Hibi, Takayuki, Trung, Ngo Viet, Zheng, Xinxian
The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining...
Symbolic powers of monomial ideals and vertex cover algebras (2005)
Herzog, Juergen, Hibi, Takayuki, Trung, Ngo Viet
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are...
Mixed multiplicities of ideals versus mixed volumes of polytopes (2005)
The main results of this paper interpret mixed volumes of lattice polytopes as mixed multiplicities of ideals and mixed multiplicities of ideals as Samuel's multiplicities. In particular, we can give...
On the regularity of products and intersections of complete intersections (2005)
Chardin, Marc, Minh, Nguyen Cong, Trung, Ngo Viet
This paper proves that the Castelnuovo-Mumford regularities of the product and sum of two monomial complete intersection ideals are at most the sum of the regularities of the two ideals, and provides...
Castelnuovo-Mumford Regularity and finiteness of Hilbert Functions (2004)
Rossi, Maria Evelina, Trung, Ngo Viet, Valla, Giuseppe
The notion of regularity has been used by S. Kleiman in the construction of bounded families of ideals or sheaves with given Hilbert polynomial, a crucial point in the construction of Hilbert or...
Huneke, Craig, Trung, Ngo Viet
Our focus in this paper is in effective computation of the core core(I) of an ideal I which is defined to be the intersection of all minimal reductions of I. The first main result is a closed formula...
Asymptotic behaviour of arithmetically Cohen-Macaulay blow-ups (2004)
This paper addresses problems related to the existence of arithmetic Macaulayfications of projective schemes. Let Y be the blow-up of a projective scheme X = Proj R along the ideal sheaf of I \subset...
Borel-fixed ideals and reduction number (2003)
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 certain specializations...
On the asymptotic linearity of Castelnuovo-Mumford regularity (2002)
Trung, Ngo Viet, Wang, Hsin-Ju
Let R be a standard graded ring over a commutative Noetherian ring with unity and I a graded ideal of R. Let M be a finitely generated graded R-module. We prove that there exist integers e and...
Castelnuovo-Mumford regularity and extended degree (2002)
Rossi, Maria Evelina, Trung, Ngo Viet, Valla, Giuseppe
The main result of this paper shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring is effectively bounded by the dimension and any extended degree. From this it follows...
Positivity of mixed multiplicities (2002)
This paper studies mixed multiplicities of an arbitrary standard bigraded algebra and mixed multiplicities of two ideals I, J in a local ring (A,m), where I is an m-primary ideal and J an arbitrary...
Hilbert polynomials of non-standard bigraded algebras (2002)
Hoang, Nguyen Duc, Trung, Ngo Viet
This paper is a systematic study of the Hilbert polynomial of a bigraded algebra R which are generated by elements of bidegrees (1,0), (d_1,1),...,(d_r,1), where d_1,...,d_r are non-negative...
Specialization of modules (2002)
Let R be a polynomial ring over k(u), where k is a field k and u is a finite family or inderterminates. The paper introduces the specialization of an arbitrary finitely generated R-module by the...
Specialization of modules over a local ring (2002)
This paper is a continuation of an earlier paper of the authors on the probem of specializations of modules. The aim here is to define specialisations of finitely generated modules over local rings...
Evaluations of initial ideals and Castelnuovo-Mumford regularity (2002)
This paper characterizes the Castelnuovo-Mumford regularity by evaluating the initial ideal with respect to the reverse lexicographic order.
Grobner bases, local cohomology and reduction number (2002)
D. Bayer and M. Stillman showed that Grobner bases can be used to compute the Castelnuovo-Mumford regularity, which is a measure for the vanishing of graded local cohomology modules. The aim of this...
Constructive characterization of the reduction numbers (2002)
We present a constructive description of minimal reductions with a given reduction number. This description has interesting consequences on the minimal reduction number, the big reduction number, and...
Groebner bases and regularity of Rees algebras (2001)
Herzog, Juergen, Popescu, Dorin, Trung, Ngo Viet
In this paper we study homological properties of the Rees ring R of the graded maximal ideal of a standard graded k-algebra A. In particular we are interested the comparison of the depth and...
Problems and algorithms for affine semigroups (2001)
Bruns, Winfried, Gubeladze, Joseph, Trung, Ngo Viet
In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems...
Asymptotic linear bounds for the Castelnuovo-Mumford regularity (2001)
Herzog, Juergen, Hoa, Le Tuan, Trung, Ngo Viet
We prove asymptotic linear bounds for the Castelnuovo-Mumford regularity of certain filtrations of homogeneous ideals whose Rees algebras need not to be Noetherian.
Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces (1997)
Conca, Aldo., Valla, Giuseppe., Herzog, Jurgen., Trung, Ngo Viet.
American Journal of Mathematics - Volume 119, Number 4, August 1997
Zur Theorie der Buchsbaum-Ringe. (1983)
Halle, Univ., Diss. B, 1983 (Nicht f.d. Austausch).