Factored arrangements of hyperplanes
type: Item
instance of: scholarly article
title: Factored arrangements of hyperplanes
zbMATH Open document ID: 0823.52013
author: Michel Jambu
author: Luis Paris
published in: Kodai Mathematical Journal
publication date: 1995-10-23T00:00:00Z
review text: The paper discusses factored arrangements \(\mathcal A\) of hyperplanes in finite-dimensional complex spaces. Roughly speaking, an arrangement \(\mathcal A\) is factored if it allows a suitable ``nice'' partition (factorization) into smaller sets of hyperplanes. The existence of a factorization translates into a factorization of the associated Orlik-Solomon algebra (cohomology algebra of the complement) and the corresponding Poincaré polynomial. An arrangement \(\mathcal A\) is inductively factored it it has a stronger kind of factorization (called inductive factorization). The authors survey and explain the results they have obtained in their paper in Eur. J. Comb. 16, No. 3, 267-292 (1995; see the review above). These include that inductively factored arrangements are free, and in the real case that the rank generating function for a certain poset which is naturally associated with the underlying chamber complex factors nicely.
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 729231
zbMATH Keywords: hyperplane arrangements
zbMATH Keywords: free arrangements
zbMATH Keywords: cohomology algebra
zbMATH Keywords: factorization
reviewed by: Egon Schulte
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138040032
OpenAlex ID: W1967358891
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DOI: 10.2996/KMJ/1138040032
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description: scientific article; zbMATH DE number 729231