Complete negatively pinched Kähler surfaces of finite volume
Let S be a 2-dimensional, complete negatively pinched Kähler manifold of finite volume. It is known that S is a quasi-projective surface and can be compactified as a normal projective space \(\hat S\) by providing each end point with one point. S is then called the Siu-Yau's one-point compactification. By means of the classification method of normal surface singularities with solvable local fundamental groups due to \textit{P. Wagreich} [Topology 11, 51-72 (1972; Zbl 0204.56404)], the author proves that \(\hat S\) has only almost simple elliptic singularities. It is also shown that the \(L^ 2\)-cohomology group \(H^*_{(2)}\) of S and the intersection homology group \(IH_*\) of \(\hat S\) are related with each other by \(H^ i_{(2)}(S)\simeq IH_{4-i}(\hat S),\) \(0\leq i\leq 4\).
scientific article; zbMATH DE number 4080334