Resurgences for ideals of special point configurations in PN coming from hyperplane arrangements

JOURNAL OF ALGEBRA

卷:443

Article

Dumnicki, M.¹  Harbourne, B.²  Nagel, U.³  Seceleanu, A.²  Szemberg, T.⁴  Tutaj-Gasinska, H.¹ 

[1] Jagiellonian Univ, Inst Math, PL-30384 Krakow, Poland

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

[3] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

[4] Inst Matemat UP, PL-30084 Krakow, Poland

关键词: Symbolic powers;    Fat points;    Homogeneous ideals;    Polynomial rings;    Projective space;   

DOI  :  10.1016/j.jalgebra.2015.07.022

来源: Elsevier

【 摘 要 】

Symbolic powers of ideals have attracted interest in commutative algebra and algebraic geometry for many years, with a notable recent focus on containment relations between symbolic powers and ordinary powers; see for example [3,7,13, 16,18-20] to cite just a few. Several invariants have been introduced and studied in the latter context, including the resurgence and asymptotic resurgence [3,15]. There have been exciting new developments in this area recently. I-r had been expected for several years that I(Nr N+1) subset of Ir should hold for the ideal / of any finite set of points in P-N for all r > 0, but in the last year various counterexamples have now been constructed (see [11,17,8]), all involving point sets coming from hyperplane arrangements. In the present work, we compute their resurgences and obtain in particular the first examples where the resurgence and the asymptotic resurgence are not equal. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free