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Freeness and multirestriction of hyperplane arrangements

Part of: Rings and algebras with additional structure Commutative algebra: Homological methods Projective and enumerative geometry

Published online by Cambridge University Press:  22 March 2012

Mathias Schulze
Mathias Schulze*
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA (email: mschulze@math.okstate.edu)
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Abstract

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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.

Keywords

hyperplane arrangementfree divisor

MSC classification

Secondary: 14N20: Configurations and arrangements of linear subspaces 16W25: Derivations, actions of Lie algebras 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 799 - 806
Copyright
Copyright © Foundation Compositio Mathematica 2012

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