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arXiv · 1307.3750

Combinatorial data of a free arrangement and the Terao conjecture

Tran Quoc Cong
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Abstract

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.

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Tran Quoc Cong. 2024-05-10. Combinatorial data of a free arrangement and the Terao conjecture. https://arxiv.org/abs/1307.3750

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