  We investigate the complement of the discriminant in the projective space
PSym^d C^{n+1} of polynomials defining hypersurfaces of degree d in P^n.
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 by Bessis and draws on results and methods
from previous work of the author addressing a comparable problem for any versal
unfolding of Brieskorn Pham singularities.
