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Mixed multiplicities of ideals versus mixed volumes of polytopes
Ngo Viet Trung, Jugal Verma
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 part…
Castelnuovo-Mumford Regularity and finiteness of Hilbert Functions
Maria Evelina Rossi, Ngo Viet Trung, Giuseppe Valla
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…
Asymptotic behaviour of arithmetically Cohen-Macaulay blow-ups
Huy Tai Ha, Ngo Viet Trung
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…
On the core of ideals
Craig Huneke, Ngo Viet Trung
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…
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…
On the asymptotic linearity of Castelnuovo-Mumford regularity
Ngo Viet Trung, Hsin-Ju Wang
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 in…