Star configurations in Pn

JOURNAL OF ALGEBRA

卷:376

Article

Geramita, A. V.^1,2  Harbourne, B.³  Migliore, J.⁴ 

[1] Queens Univ, Dept Math, Kingston, ON, Canada

[2] Univ Genoa, Dipartimento Matemat, Genoa, Italy

[3] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[4] Univ Notre Dame, Dept Math, South Bend, IN USA

关键词: Star configurations;    Symbolic power;    Basic double G-link;    Arithmetically Cohen-Macaulay;    ACM;    Primary decomposition;    Resurgence;   

DOI  :  10.1016/j.jalgebra.2012.11.034

来源: Elsevier

【 摘 要 】

Star configurations are certain unions of linear subspaces of projective space. They have appeared in several different contexts: the study of extremal Hilbert functions for fat point schemes in the plane; the study of secant varieties of some classical algebraic varieties; the study of the resurgence of projective schemes. In this paper we study some algebraic properties of the ideals defining star configurations, including getting partial results about Hilbert functions, generators and minimal free resolutions of the ideals and their symbolic powers. We also show that their symbolic powers define arithmetically Cohen-Macaulay subschemes and we obtain results about the primary decompositions of the powers of the ideals. As an application, we compute the resurgence for the ideal of the codimension n - 1 star configuration in P-n in the monomial case (i.e., when the number of hyperplanes is n + 1). (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free