The moduli space of 3-folds with \(K=0\) may nevertheless be irreducible
type: Item
instance of: scholarly article
title: The moduli space of 3-folds with \(K=0\) may nevertheless be irreducible
zbMATH Open document ID: 0649.14021
DOI: 10.1007/BF01458074
author: Miles Reid
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164295
review text: 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).
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 4059576
zbMATH Keywords: complex analytic 3-fold
zbMATH Keywords: Hodge numbers
zbMATH Keywords: moduli space
zbMATH Keywords: K3-surfaces
Wikidata QID: Q55895124
reviewed by: Mauro C. Beltrametti
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4059576