Compositio Mathematica

Table of Contents - May 2012 - Volume 148, Issue 03  

Research Article

Freeness and multirestriction of hyperplane arrangements

Mathias Schulzea1

a1 Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA (email: mschulze@math.okstate.edu)

Abstract

Generalizing a result of Yoshinaga in dimension three, we show that a central hyperplane arrangement in 4-space is free exactly if its restriction with multiplicities to a fixed hyperplane of the arrangement is free and its reduced characteristic polynomial equals the characteristic polynomial of this restriction. We show that the same statement holds true in any dimension when imposing certain tameness hypotheses.

(Received April 29 2011)

(Accepted October 18 2011)

(Online publication March 22 2012)

2010 Mathematics Subject Classification

  • 14N20 (primary);
  • 16W25;
  • 13D40 (secondary)

Keywords

  • hyperplane arrangement;
  • free divisor

Footnotes

The author gratefully acknowledges support by the ‘SQuaREs’ program of American Institute of Mathematics. He would like to thank Graham Denham, Hal Schenck, Max Wakefield, and Uli Walther for helpful discussions.