Hurwitz stabilisers of some short redundant Artin systems for the braid group Br₃

We investigate the Hurwitz action of the braid group Br_n on the n-fold Cartesian product of Br_3 and determine some stabilisers of its Artin systems. Our algebraic result is complemented by a geometric study of families of plane polynomial coverings of degree 3. Together they lead to characterisations of the set of 'paths realised by degenerations' of the polynomials as defined by Donaldson in 'Polynomials, vanishing cycles and Floer homology'.