On proximity relations for valuations dominating a two-dimensional regular local ring

On the value-semigroup of a simple complete ideal in a two-dimensional regular local ring

Let R be a two-dimensional regular local ring with maximal ideal m, and let ℘ be a simple complete m-primary ideal which is residually rational. Let R0 := R $ R1 $ · · · $ Rr be the quadratic sequence associated to ℘, let Γ℘ be the value-semigroup associated to ℘, and let (ej(℘))0≤j≤r be the multiplicity sequence of ℘. We associate to ℘ a sequence (γi(℘))0≤i≤g of natural integers which we call ...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

The Leading Ideal of a Complete Intersection of Height Two in a 2-dimensional Regular Local Ring

Let (S,n) be a 2-dimensional regular local ring and let I = (f, g) be an ideal in S generated by a regular sequence f, g of length two. Let I∗ be the leading ideal of I in the associated graded ring grn(S), and set R = S/I and m = n/I. In [GHK2], we prove that if μG(I ∗) = n, then I∗ contains a homogeneous system {ξi}1≤i≤n of generators such that deg ξi + 2 ≤ deg ξi+1 for 2 ≤ i ≤ n−1, and htG(ξ...

Cores of Ideals in Two Dimensional Regular Local

The main result of this paper is the explicit determination of the core of integrally closed ideals in two-dimensional regular local rings. The core of an ideal I in a ring R was introduced by Judith Sally in the late 1980's and alluded to in Rees and Sally's paper RS]. Recall that a reduction of I is any ideal J for which there exists an integer n such that JI n = I n+1 NR]. In other words, J ...

Quantum transport on two-dimensional regular graphs

Abstract. We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem can be treated in a large measure analytically. Some of these results carry over to graphs which obey open boundary conditions (OBCs), such as cylind...