Lê Tuân Hoa

On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals

Abstract In the first part of this paper we show that the Castelnuovo-Mumford regularity of a monomial ideal is bounded above by its arithmetic degree. The second part gives upper bounds for the Castelnuovo-Mumford regularity and the arithmetic degree of a monomial ideal in terms of the degrees of its generators. These bounds can be formulated for an arbitrary homogeneous ideal in terms of any Gröbner basis.

Castelnuovo–Mumford regularity of simplicial toric rings

Abstract Bounds for the Castelnuovo–Mumford regularity of simplicial toric rings are given which are close to the bound stated in Eisenbud–Gotos Conjecture.

Castelnuovo–Mumford regularity of initial ideals

Abstract A bound is given for the Castelnuovo–Mumford regularity of initial ideals of a homogeneous ideal in a polynomial ring over an infinite field of any characteristic. The bound depends neither on term orders nor on the coordinates. If the ideal is perfect, then a much better bound is also provided.

Castelnuovo–Mumford Regularity of Some Modules

We give bounds for the Castelnuovo–Mumford regularity of the so-called sequentially κ-Buchsbaum modules and of the canonical modules of certain rings.

Castelnuovo–Mumford Regularity of Sums of Powers of Polynomial Ideals

The asymptotic behavior of the Castelnuovo–Mumford regularity of sums of powers of polynomial ideals is studied. It is shown that as well as are bounded by linear functions of n provided dim S/(I + I 1 +···+ I p ) ≤ 1. When I 1,…, I p are monomial ideals such that dim S/(I 1 +···+ I p ) = 0, we also show that is not necessarily an asymptotically linear function of n, but the limit always exists.