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

M. Dumnicki, B. Harbourne, U. Nagel, A. Seceleanu, T. Szemberg, H. Tutaj-Gasińska

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

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. It had been expected for several years that I(Nr-N+1)⊆Ir should hold for the ideal I of any finite set of points in PN 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.

Original languageEnglish
Pages (from-to)383-394
Number of pages12
JournalJournal of Algebra
Volume443
DOIs
StatePublished - Dec 1 2015

Bibliographical note

Funding Information:
The second author's work on this project was sponsored by the National Security Agency under Grant/Cooperative agreement “Topics in Algebra and Geometry, Curves and Containments” Number H98230-13-1-0213 . The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notice. The work of the third author was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 . The first, fifth and sixth author's research was partially supported by the National Science Centre , Poland, grant 2014/15/B/ST1/02197 . We also thank the referee for helpful comments and corrections.

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

  • Fat points
  • Homogeneous ideals
  • Polynomial rings
  • Projective space
  • Symbolic powers

ASJC Scopus subject areas

  • Algebra and Number Theory

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