  We define for every affine Coxeter graph a certain factor group of the
associated Artin group and prove that some of these groups appear as orbifold
fundamental groups of moduli spaces. Examples are the moduli space of
nonsingular cubic algebraic surfaces and the universal nonhyperelliptic smooth
genus three curve. We use this to obtain a simple presentation of the mapping
class group of a compact genus three topological surface with connected
boundary. This leads to a modification of Wajnryb's presentation of the mapping
class groups in the higher genus case that can be understood in
algebro-geometric terms.
