  We study those Artin groups which, modulo their centers, are finite index
subgroups of the mapping class group of a sphere with at least 5 punctures. In
particular, we show that any injective homomorphism between these groups is
parameterized by a homeomorphism of a punctured sphere together with a map to
the integers. We also give a generating set for the automorphism group of the
pure braid group on at least 4 strands. The technique, following Ivanov, is to
prove that every superinjective map of the complex of curves of a sphere with
at least 5 punctures is induced by a homeomorphism.
