The characteristic polynomial of a multiarrangement

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dc.creatorAbe, Takuro
dc.creatorTerao, Hiroaki
dc.creatorWakefield, Max
dc.date2006-11-24
dc.date.accessioned2026-07-07T08:35:13Z
dc.date.available2026-07-07T08:35:13Z
dc.descriptionGiven a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using this polynomial we define the characteristic polynomial of a multiarrangement which generalizes the characteristic polynomial of an arragnement. The characteristic polynomial of an arrangement is a combinatorial invariant, but this generalized characteristic polynomial is not. However, when the multiarrangement is free, we are able to prove the factorization theorem for the characteristic polynomial. The main result is a formula that relates `global' data to `local' data of a multiarrangement given by the coefficients of the respective characteristic polynomials. This result gives a new necessary condition for a multiarrangement to be free. Consequently it provides a simple method to show that a given multiarrangement is not free.
dc.description12 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0611742
dc.identifierhttp://arxiv.org/abs/math/0611742
dc.identifierAdvances in Math. 215 (2007), 825-838
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139677
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject32S22 (Primary) 14N20, 52C35 (Secondary)
dc.titleThe characteristic polynomial of a multiarrangement
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