The characteristic polynomial of a multiarrangement

DOI10.1016/j.aim.2007.04.019zbMath1123.52012arXivmath/0611742OpenAlexW1965693448WikidataQ126252567 ScholiaQ126252567MaRDI QIDQ2383010

Takuro Abe, Hiroaki Terao, Max D. Wakefield

Publication date: 5 October 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611742

zbMATH Keywords

characteristic polynomialderivationsHilbert seriesHyperplane arrangementfree multiarrangement

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35)

Related Items (23)

Divisionally free arrangements of hyperplanes ⋮ Freeness and multirestriction of hyperplane arrangements ⋮ Heavy hyperplanes in multiarrangements and their freeness ⋮ Free multiplicities on the moduli of \(X_{3}\) ⋮ Plus-one Generated and Next to Free Arrangements of Hyperplanes ⋮ A residual duality over Gorenstein rings with application to logarithmic differential forms ⋮ Chambers of 2-affine arrangements and freeness of 3-arrangements ⋮ Recent topics of arrangements of hyperplanes ⋮ Inequalities for free multi-braid arrangements ⋮ Splitting types of bundles of logarithmic vector fields along plane curves ⋮ Free arrangements and coefficients of characteristic polynomials ⋮ A homological characterization for freeness of multi-arrangements ⋮ Characteristic polynomials, \(\eta \)-complexes and freeness of tame arrangements ⋮ Freeness of hyperplane arrangements and related topics ⋮ Exponents of 2-multiarrangements and multiplicity lattices ⋮ Free and non-free multiplicity on the deleted \(A_{3}\) arrangement ⋮ Locally heavy hyperplanes in multiarrangements ⋮ Deletion theorem and combinatorics of hyperplane arrangements ⋮ Generalized splines and graphic arrangements ⋮ Roots of characteristic polynomials and intersection points of line arrangements ⋮ Totally free arrangements of hyperplanes ⋮ Coxeter multiarrangements with quasi-constant multiplicities ⋮ Free and non-free multiplicities on the \(A_3\) arrangement

Uses Software

• Macaulay2

Cites Work

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• A formula for the characteristic polynomial of an arrangement
• Characterization of a free arrangement and conjecture of Edelman and Reiner
• Free arrangements of hyperplanes over an arbitrary field
• Generalized exponents of a free arrangement of hyperplanes and Shepherd- Todd-Brieskorn formula
• Hilbert polynomials and geometric lattices
• Multiderivations of Coxeter arrangements
• The primitive derivation and freeness of multi-Coxeter arrangements.
• Derivations of an effective divisor on the complex projective line
• Free and Locally Free Arrangements with a Given Intersection Lattice
• ON THE FREENESS OF 3-ARRANGEMENTS
• The Euler multiplicity and addition-deletion theorems for multiarrangements
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• The module of logarithmic \(p\)-forms of a locally free arrangement

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