Advanced Studies in Pure Mathematics

Hyperplane arrangements: computations and conjectures

Hal Schenck

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This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as Koszul and Lie algebra methods, homological techniques, and the Bernstein–Gelfand–Gelfand correspondence, all illustrated with concrete calculations. We also explore connections of arrangements to other areas, such as De Concini–Procesi wonderful models, the Feichtner–Yuzvinsky algebra of an atomic lattice, fatpoints and blowups of projective space, and plane curve singularities.

Article information

Arrangements of Hyperplanes — Sapporo 2009, H. Terao and S. Yuzvinsky, eds. (Tokyo: Mathematical Society of Japan, 2012), 323-358

Received: 29 October 2009
Revised: 1 March 2011
First available in Project Euclid: 24 November 2018

Permanent link to this document euclid.aspm/1543085014

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22]
Secondary: 13D02: Syzygies, resolutions, complexes 16E05: Syzygies, resolutions, complexes 16S37: Quadratic and Koszul algebras 20F14: Derived series, central series, and generalizations


Schenck, Hal. Hyperplane arrangements: computations and conjectures. Arrangements of Hyperplanes — Sapporo 2009, 323--358, Mathematical Society of Japan, Tokyo, Japan, 2012. doi:10.2969/aspm/06210323.

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