  This paper considers the question of relative hyperbolicity of an Artin group
with regard to the geometry of its associated Deligne complex. We prove that an
Artin group is weakly hyperbolic relative to its finite (or spherical) type
parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic
space. For a 2-dimensional Artin group the Deligne complex is Gromov hyperbolic
precisely when the corresponding Davis complex is Gromov hyperbolic, that is,
precisely when the underlying Coxeter group is a hyperbolic group. For Artin
groups of FC type we give a sufficient condition for hyperbolicity of the
Deligne complex which applies to a large class of these groups for which the
underlying Coxeter group is hyperbolic.
