Abelianisation of orthogonal groups and the fundamental group of modular varieties

V Gritsenko, K Hulek, Gregory K Sankaran

Research output: Contribution to journalArticle

17 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)463-478
Number of pages16
JournalJournal of Algebra
Issue number2
Early online date19 Mar 2009
Publication statusPublished - 15 Jul 2009



  • Modular variety
  • Orthogonal groups
  • Commutator subgroup

Cite this