Zariski theorems and diagrams for braid groups

Details Zariski theorems and diagrams for braid groups Zariski theorems and diagrams for braid groups

2000-10-31

arxiv.org/abs/math/0010323v2

Mathematics

Group Theory

21 pages

Scientific paper

10.1007/s002220100155

Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Brou\'e-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the classification. The two ingredients are Springer theory of regular elements and a Zariski-like theorem.

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