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# Asian Journal of Mathematics

## Volume 19 (2015)

### Number 4

### Topological classification of simplest Gorenstein non-complete intersection singularities of dimension 2

Pages: 651 – 792

DOI: http://dx.doi.org/10.4310/AJM.2015.v19.n4.a4

#### Authors

#### Abstract

Let $p$ be normal singularity of the 2-dimensional Stein space $V$. Let $\pi : M \to V$ be a minimal good resolution of $V$, such that the irreducible components $A_i$ of $A = \pi^{-1}(p)$ are nonsingular and have only normal crossings. Associated to $A$ is weighted dual graph $\Gamma$ which, along with the genera of the $A_i$, fully describes the topology and differentiable structure of $A$ and the topological and differentiable nature of the embedding of $A$ in $M$. It is well known that the simplest Gorenstein non-complete intersection singularities of dimension two are exactly those minimal elliptic singularities with fundamental cycle self intersection number $-5$. In this paper we classify all weighted dual graphs of these singularities. In particular, we prove that there is no integral homology link structure in the class of simplest Gorenstein non-complete intersection singularities of dimension two.

#### Keywords

normal singularities, topological classification, weighted dual graph

#### 2010 Mathematics Subject Classification

Primary 32S25. Secondary 14B05, 58K65.