Analytic compactification of \(\mathbb C^2/\mathbb D\) (Q2479812)

The authors consider minimal analytic compactifications \((\widehat{M}, C)\) of surfaces \(X\) that are quotients of \(\mathbb{C}\) modulo small finite subgroups of \(\text{GL}(2, \mathbb{C})\). These compactifications of \(X\) are minimal with regards to the structure of certain \(-1\) curves on the boundary \(C\) (for a precise definition, see the text of this article or [\textit{J. A. Morrow}, Rice Univ. Studies 59, No. 1 (Proc. Conf. Complex Analysis 1972, I), 97--112 (1973; Zbl 0277.32019)]). In particular, the authors prove a theorem describing the dual graph of a minimal resolution of \((\widehat{M}, C)\) the minimal normal analytic compactification of \(X\). This builds upon work done in [\textit{M. Abe, M. Furushima} and \textit{T. Shima}, Abh. Math. Semin. Univ. Hamb. 74, 223--235 (2004; Zbl 1062.32012) and \textit{M. Abe, M. Furushima} and \textit{M. Yamasaki}, Kyushu J. Math. 54, No. 1, 87--101 (2000; Zbl 1045.32020)].