Affine Artin groups and the fundamental groups of some moduli spaces

Details Affine Artin groups and the fundamental groups of some moduli spaces Affine Artin groups and the fundamental groups of some moduli spaces

1998-01-26

arxiv.org/abs/math/9801117v2

Mathematics

Algebraic Geometry

This is a substantial revision of the previous version with some of the proofs simplified and the exposition (we hope) improve

Scientific paper

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.

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