Abelianisation of orthogonal groups and the fundamental group of modular varieties

V Gritsenko; K Hulek; Gregory K Sankaran

doi:10.1016/j.jalgebra.2009.01.037

Abelianisation of orthogonal groups and the fundamental group of modular varieties

V Gritsenko, K Hulek, Gregory K Sankaran

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

52 Citations (SciVal)

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.

Original language	English
Pages (from-to)	463-478
Number of pages	16
Journal	Journal of Algebra
Volume	322
Issue number	2
Early online date	19 Mar 2009
DOIs	https://doi.org/10.1016/j.jalgebra.2009.01.037
Publication status	Published - 15 Jul 2009

Keywords

Modular variety
Orthogonal groups
Commutator subgroup

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10.1016/j.jalgebra.2009.01.037

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title = "Abelianisation of orthogonal groups and the fundamental group of modular varieties",

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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AU - Hulek, K

AU - Sankaran, Gregory K

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N2 - 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.

AB - 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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KW - Orthogonal groups

KW - Commutator subgroup

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DO - 10.1016/j.jalgebra.2009.01.037

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VL - 322

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JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Abelianisation of orthogonal groups and the fundamental group of modular varieties

Abstract

Keywords

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