Search results for "Macau"

The minimal free resolution of fat almost complete intersections in ℙ1 x ℙ1

2017

AbstractA current research theme is to compare symbolic powers of an ideal I with the regular powers of I. In this paper, we focus on the case where I = IX is an ideal deûning an almost complete intersection (ACI) set of points X in ℙ1 × ℙ1. In particular, we describe a minimal free bigraded resolution of a non-arithmetically Cohen-Macaulay (also non-homogeneous) set 𝒵 of fat points whose support is an ACI, generalizing an earlier result of Cooper et al. for homogeneous sets of triple points. We call 𝒵 a fat ACI.We also show that its symbolic and ordinary powers are equal, i.e, .

Rivestimenti di varietà algebriche contenuti in fibrati di piani proiettivi

Studies on Macau Gaming Law

2012

The volume collects different essays on different aspects of Macau gaming law

Regulation of Gaming Companies in Macau

2012

The article examines the way to incorporate and manage gaming companies in Macau.

XVIII International Congress of Comparative Law : Macau Regional Reports

2010

Macau contributions to the congress of the International Academy of Comparative Law

The use of comparative law by the judiciary in Macao

2013

The article examines to which extent judges in Macau resort to comparative analysis for their judgements.

Tower sets and other configurations with the Cohen-Macaulay property

2014

Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes …

Ideals generated by the inner 2-minors of collections of cells

2023

In 2012 Ayesha Asloob Qureshi connected collections of cells to Commutative Algebra assigning to every collection $\mathcal{P}$ of cells the ideal of inner 2-minors, denoted by $I_{\mathcal{P}}$, in the polynomial ring $S_{\mathcal{P}}=K[x_v:v\text{ is a vertex of }\mathcal{P}]$. Investigating the main algebraic properties of $K[\mathcal{P}]=S_{\mathcal{P}}/I_{\mathcal{P}}$ depending on the shape of $\mathcal{P}$ is the purpose of this research. Many problems are still open and they seem to be fascinating and exciting challenges.\\ In this thesis we prove several results about the primality of $I_{\mathcal{P}}$ and the algebraic properties of $K[\mathcal{P}]$ like Cohen-Macaulyness, normali…

On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces

2017

We study the arithmetically Cohen-Macaulay (ACM) property for finite sets of points in multiprojective spaces, especially ( P 1 ) n (\mathbb P^1)^n . A combinatorial characterization, the ( ⋆ ) (\star ) -property, is known in P 1 × P 1 \mathbb P^1 \times \mathbb P^1 . We propose a combinatorial property, ( ⋆ s ) (\star _s) with 2 ≤ s ≤ n 2\leq s\leq n , that directly generalizes the ( ⋆ ) (\star ) -property to ( P 1 ) n (\mathbb P^1)^n for larger n n . We show that X X is ACM if and only if it satisfies the ( ⋆ n ) (\star _n) -property. The main tool for several of our results is an extension to the multiprojective setting of certain liaison methods in projective space.

Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1

2019

In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.