The characteristic polynomial of a multiarrangement

Takuro Abe, Hiroaki Terao, Max Wakefield

研究成果: Contribution to journalArticle査読

24 被引用数 (Scopus)

抄録

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 arrangement. 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.

本文言語英語
ページ(範囲)825-838
ページ数14
ジャーナルAdvances in Mathematics
215
2
DOI
出版ステータス出版済み - 11 10 2007
外部発表はい

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

フィンガープリント

「The characteristic polynomial of a multiarrangement」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル