Combinatorial data of a free arrangement and the Terao conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2013
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| _version_ | 1866913345428258816 |
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| author | Cong, Tran Quoc |
| author_facet | Cong, Tran Quoc |
| contents | We present a combinatorial structure of generators of $D(\mathcal{A}).$ This structure permits us to detect the relationship between the combinatorial determined property and the singularity of vector field. Consequently, by using only combinatorial data, we have a basis of the module in free case and that yields a proof for the Terao's conjecture. We also verify the example of Ziegler and give a sufficient condition on combinatorial determined property of generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1307_3750 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Combinatorial data of a free arrangement and the Terao conjecture Cong, Tran Quoc Combinatorics We present a combinatorial structure of generators of $D(\mathcal{A}).$ This structure permits us to detect the relationship between the combinatorial determined property and the singularity of vector field. Consequently, by using only combinatorial data, we have a basis of the module in free case and that yields a proof for the Terao's conjecture. We also verify the example of Ziegler and give a sufficient condition on combinatorial determined property of generators. |
| title | Combinatorial data of a free arrangement and the Terao conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1307.3750 |