Hurwitz stabilisers of some short redundant Artin systems for the braid group Br3
Abstract
We investigate the Hurwitz action of the braid group Brn on the n-fold Cartesian product of Br3 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'.
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