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The freeness and minimal free resolutions of modules of differential operators of a generic hyperplane arrangement
| Title: | The freeness and minimal free resolutions of modules of differential operators of a generic hyperplane arrangement |
| Authors: | Nakashima, Norihiro Browse this author | | Okuyama, Go Browse this author | | Saito, Mutsumi Browse this author →KAKEN DB |
| Keywords: | Ring of differential operators | | Generic hyperplane arrangement | | Minimal free resolution | | Jacobian ideal | | Jet module |
| Issue Date: | 1-Feb-2012 |
| Publisher: | Elsevier |
| Journal Title: | Journal of Algebra |
| Volume: | 351 |
| Issue: | 1 |
| Start Page: | 294 |
| End Page: | 318 |
| Publisher DOI: | 10.1016/j.jalgebra.2011.10.042 |
| Abstract: | Let A be a generic hyperplane arrangement composed of r hyperplanes in an n-dimensional vector space, and S the polynomial ring in n variables. We consider the S-submodule D(m)(A) of the nth Weyl algebra of homogeneous differential operators of order m preserving the defining ideal of A. We prove that if n ≥ 3, r > n, m > r - n + 1, then D(m)(A) is free (Holm's conjecture). Combining this with some results by Holm, we see that D(m)(A) is free unless n ≥ 3, r > n, m < r - n + 1. In the remaining case, we construct a minimal free resolution of D(m)(A) by generalizing Yuzvinsky's construction for m = 1. In addition, we construct a minimal free resolution of the transpose of the m-jet module, which generalizes a result by Rose and Terao for m = 1. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/48291 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 齋藤 睦
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