Abelianisation of orthogonal groups and the fundamental group of modular varieties

Reference:

Gritsenko, V., Hulek, K. and Sankaran, G. K., 2009. Abelianisation of orthogonal groups and the fundamental group of modular varieties. Journal of Algebra, 322 (2), pp. 463-478.

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Official URL:

http://dx.doi.org/10.1016/j.jalgebra.2009.01.037

Abstract

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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