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On Ricci flat 3-fold. (English) Zbl 0649.14024
The authors study a particular class of algebraic 3-folds with trivial canonical bundle, obtained as follows. Let G be a cyclic group of order d of automorphisms of a 3-dimensional torus T, such that 0 is an isolated fixed point of G, G acts freely near 0 and \(\det (dg)_ 0=1\) for all \(g\in G\). In this case the authors show that the minimal desingularization \(T^{\wedge}/G\) of T/G is a projective 3-fold with trivial canonical bundle, moreover they give a complete classification of such T/G’s proving that they can be obtained as quotients from three standard examples.
The proof is based on an explicit construction of a minimal desingularization of \({\mathbb{C}}\) 3/G (where \(G=<\psi >\), \(\psi\) linear transformation of order d) by the method of the toroidal embeddings.
Reviewer: L.Picco Botta

MSC:
14J30 \(3\)-folds
14L30 Group actions on varieties or schemes (quotients)
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
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