Abelianisation of orthogonal groups and the fundamental group of modular varieties

Details Abelianisation of orthogonal groups and the fundamental group of modular varieties Abelianisation of orthogonal groups and the fundamental group of modular varieties

2008-10-09

arxiv.org/abs/0810.1614v1

Mathematics

Algebraic Geometry

Scientific paper

We study the commutator subgroup of integral orthogonal groups belonging to
indefinite quadratic forms. We show that the index of this commutator is 2 for
many groups that occur in the construction of moduli spaces in algebraic
geometry, in particular the moduli of K3 surfaces. We give applications to
modular forms and to computing the fundamental groups of some moduli spaces.

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