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THE CHARACTERISTIC POLYNOMIAL OF A MULTIARRANGEMENT

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83968

Title: THE CHARACTERISTIC POLYNOMIAL OF A MULTIARRANGEMENT
Authors: ABE, TAKURO Browse this author
TERAO, HIROAKI Browse this author
WAKEFIELD, MAX Browse this author
Issue Date: 2006
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 818
Start Page: 1
End Page: 12
Abstract: Given 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69626
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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