In this paper,the containment problem for the defining ideal of a special type of zero-dimensional subscheme of P^2,the so-called quasi star configuration,is investigated.Some sharp bounds for the resurgence of these ...In this paper,the containment problem for the defining ideal of a special type of zero-dimensional subscheme of P^2,the so-called quasi star configuration,is investigated.Some sharp bounds for the resurgence of these types of ideals are given.As an application of this result,for every real number 0<ε<1/2,we construct an infinite family of homogeneous radical ideals of points in K[P^2]such that their resurgences lie in the interval[2-ε,2).Moreover,the Castelnuovo-Mumford regularity of all ordinary powers of defining ideal of quasi star configurations are determined.In particular,it is shown that all of these ordinary powers have a linear resolution.展开更多
文摘In this paper,the containment problem for the defining ideal of a special type of zero-dimensional subscheme of P^2,the so-called quasi star configuration,is investigated.Some sharp bounds for the resurgence of these types of ideals are given.As an application of this result,for every real number 0<ε<1/2,we construct an infinite family of homogeneous radical ideals of points in K[P^2]such that their resurgences lie in the interval[2-ε,2).Moreover,the Castelnuovo-Mumford regularity of all ordinary powers of defining ideal of quasi star configurations are determined.In particular,it is shown that all of these ordinary powers have a linear resolution.
