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The moduli space of 3-folds with \(K=0\) may nevertheless be irreducible. (English) Zbl 0649.14021
Let X be a complex analytic 3-fold having the following properties: (i) X has at worst canonical singularities; (ii) \(K_ X=0;\) (iii) for any analytic set \(Y\subset X\) of codimension \(\geq 2\), \(\pi_ 1(X-Y)=0\); (iv) if X is non-singular, its Hodge numbers are \[ \begin{matrix} 1& 0& 0& 1 \\ 0& h^{1,2}& B_ 2& 0\\ 0& B_ 2& h^{1,2}& 0\\ 1& 0& 0& 1 \end{matrix}. \] As the author says, the main point of the paper is to suggest a speculative framework in which the birational classes of 3-folds X satisfying these conditions might all fit together into an irreducible moduli space (such 3-folds are “equivalent” to K3-surfaces).
Reviewer: M.Beltrametti

MSC:
14J30 \(3\)-folds
14D20 Algebraic moduli problems, moduli of vector bundles
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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