Hurwitz stabilisers of some short redundant Artin systems for the braid group Br_3

Details Hurwitz stabilisers of some short redundant Artin systems for the braid group Br_3 Hurwitz stabilisers of some short redundant Artin systems for the braid group Br_3

2004-06-08

arxiv.org/abs/math/0406154v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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'.

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