Gorenstein log del Pezzo surfaces. II
[For part I see the authors, J. Algebra 118, No. 1, 63-84 (1988; Zbl 0664.14019)] A projective normal surface \(\overline V\) is a Gorenstein log Del Pezzo surface if it has only rational double singularities and the canonical divisor is ample. In the paper under review, the fundamental group of the smooth part of such a surface is determined. Main result: Let \(f : V \to \overline V\) be a minimal resolution and let \(D : = f^{-1} (\text{Sing} (\overline V))\), where \(\text{Sing}(\overline V)\) is the singular locus. Let \(V^ 0 : = \overline V -\text{Sing} (\overline V)\). Then the fundamental group \(\pi_ 1 (V^ 0)\) of the smooth part \(V^ 0\) is an abelian group of order \(\leq 9\). In the paper are also classified Gorenstein log Del Pezzo surfaces, \(\overline V\), under the assumption that \(\overline V\) is relatively minimal. Existence results are also given.
scientific article; zbMATH DE number 495544