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“Weakly” elliptic Gorenstein singularities of surfaces. (English) Zbl 0934.32018
Let \(p\) be a singularity of a normal two-dimensional analytic surface \(X\) and \(\chi (D)\) be the Euler-characteristic of any cycle \(D\) and \(p_g=h^1 (M, {\Theta}_M)\).
M. Artin proved for rational singularities that \((X, p)\) is rational if and only if \(\chi = (Z_{\text{num}})=1\) and if and only if \(\min_{D\geq 0} \chi (D) \geq 1\). P. Wagreich proved that \((X, p)\) is elliptic if and only if \(\chi (Z_{\text{num}})=0\) and if and only if \(\min_{D\geq 0} \chi (D) = 0\). Later H. Laufer proved that the Gorenstein singularities with \(p_g =1\) can be characterized topologically, and for these singularities all the above analytical invariants are topological.
The author of this paper shows that for Gorenstein singularities with \(H^1 (A, Z) = 0\) the Artin- Laufer program can be continued and gives the complete answer in the case of elliptic singularities.

MSC:
32S15 Equisingularity (topological and analytic)
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
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