Zariski theorems and diagrams for braid groups

Empirical properties of generating systems for complex reflection groups an d their braid groups have been observed by Orlik-Solomon and Broue-Malle-Ro uquier, using Shephard-Todd classification. We give a general existence res ult for presentations of braid groups, which partially explains and general izes the known empirical properties. Our approach is invariant-theoretic an d does not use the classification. The two ingredients are Springer theory of regular elements and a Zariski-like theorem.