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Hokkaido University Preprint Series in Mathematics >
Periodicity of hyperplane arrangements with integral coefficients modulo positive integers
| Title: | Periodicity of hyperplane arrangements with integral coefficients modulo positive integers |
| Authors: | Kamiya, Hidehiko Browse this author | | Takemura, Akimichi Browse this author | | Terao, Hiroaki Browse this author |
| Keywords: | characteristic polynomial | | Ehrhart quasi-polynomial | | elementary divisor | | hyperplane arrangement | | intersection lattice |
| Issue Date: | 30-Mar-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 839 |
| Start Page: | 1 |
| End Page: | 14 |
| Abstract: | We study central hyperplane arrangements with integral coefficients modulo positive integers q. We prove that the cardinality of the complement of the hyperplanes is a quasi-polynomial in two ways, first via the theory of elementary divisors and then via the theory of the Ehrhart quasi-polynomials. This result is useful for determining the characteristic polynomial of the corresponding real arrangement. With the former approach, we also prove that intersection lattices modulo q are periodic except for a finite number of q’s. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69648 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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