Vol. 52, No. 2, 1974

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Fundamental groups of compact complete locally affine complex surfaces. II

John Herman Scheuneman

Vol. 52 (1974), No. 2, 553–566

The present article is a continuation of a recent paper by J. P. Fillmore and the author on properly-acting groups Γ of complex affine motions of C2 such that ΓC2 is compact. In that paper, it was proved that such a group has a normal subgroup Γ0 of finite index which is either free abelian of rank four or has generators A,B,C,D, with relations

ABA  −1B−1 = Ck(k ≧ 1)

and C and D central.

Here we build on this description up to finite index to determine the groups Γ themselves.

Mathematical Subject Classification 2000
Primary: 32M10
Secondary: 20E40
Received: 12 August 1973
Published: 1 June 1974
John Herman Scheuneman