ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14 Stagnaro, Ezio, University of Padua, Italy Pluricanonical maps of two general type threefolds with p_{g} = 0 Let X be a non-singular algebraic threefold obtained as desingularization of a degree six hypersurface V_{6} ⊂ ℙ_{ℂ}^{4}. Let us consider two different singularities on V_{6}: I) triple point with infinitely near triple curve; II) triple point with infinitely near double surface. If we impose on V_{6} five singularities of type I) in a suitable position, from the theory of canonical and pluricanonical adjoints to V_{6}, we obtain a general type threefold X having q_{1} = q_{2} = p_{g} = 0, P_{2} = 5, canonical divisor K_{X} not simultaneously big and nef, φ_{|2K_{X}|} birational. If we impose on V_{6} five singularities of type II) in a suitable position, we obtain a general type threefold having the same properties of the above threefold except P_{2} = 1 and φ_{|mK_{X}|} birational iff m ≥ 11.