2017/03/08 by Hassan Haghighi, Haghighi, Hassan, Mohammad Mosakhani +1
Computer Science · Mathematics · #13A15 #13F20 #14N05 (Secondary) #14N20 (Primary) #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1703.02827
openalex publication_date 2017/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the containment problem for the defining ideal of a special type of zero dimensional subschemes of ℙ2, so called quasi star configurations, 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 \mathbbK[ℙ2] 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, %the defining ideal of a quasi star configuration, and all of them have linear resolution.