Abstract
We investigate the complement of the discriminant in the projective space PSymdCn+1 of polynomials defining hypersurfaces of degree d in Pn. Following the ideas of Zariski, we are able to give a presentation for the fundamental group of the discriminant complement which generalises the well-known presentation in case n=1 (i.e., of the spherical braid group on d strands). In particular, our argument proceeds by a geometric analysis of the discriminant polynomial as proposed in [Be] and draws on results and methods from [L1] addressing a comparable problem for any versal unfolding of Brieskorn-Pham singularities
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