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Kleine Auflösungen spezieller dreidimensionaler Varietäten. (Small resolutions of special threefolds). (German) Zbl 0657.14021
Bonn. Math. Schr. 186, -119 (1987).
In this paper the small resolutions for 3-folds with only isolated singularities are extensively studied, mainly in order to find a characterization of the projective ones.
The author considers at first the hypersurfaces in \({\mathbb{P}}^ 4\) and the double solids with only ordinary double points; in particular he studies in details Chmutov-threefolds, cubics and quartics in \({\mathbb{P}}^ 4\), double solids with a Kummer surface as ramification surface. - Then he studies some special cases of 3-folds with higher singularities.
The main tool used for the proofs is the notion of “defect”, introduced by C. H. Clemens in his fundamental paper [Adv. Math. 47, 107-230 (1983; Zbl 0509.14045)].
Reviewer: L.Picco Botta

MSC:
14J30 \(3\)-folds
14E15 Global theory and resolution of singularities (algebro-geometric aspects)