The fundamental group at infinity of affine surfaces (Q1076751)

The authors examine smooth, contractible affine surfaces V, defined over the complex numbers. Using techniques of \textit{C. P. Ramanujam} [Ann. Math., II. Ser. 94, 69-88 (1971; Zbl 0218.14021)] they study the fundamental group at infinity of V. They show this cannot be a finite non-trivial group. For example, the following result is proved: If V is affine, irreducible and non-singular \((a)\quad whose\) coordinate ring is UFD with only constant units, \((b)\quad for\) some projective compactification, \(V\subset X\), \(P_ g(X)=0\), and \((c)\quad the\) fundamental group at infinity is finite, then V is \({\mathbb{C}}^ 2\).