Threefolds with Vanishing Hodge Cohomology
نویسنده
چکیده
We consider algebraic manifolds Y of dimension 3 over C with H(Y,ΩjY ) = 0 for all j ≥ 0 and i > 0. Let X be a smooth completion of Y with D = X − Y , an effective divisor on X with normal crossings. If the D-dimension of X is not zero, then Y is a fibre space over a smooth affine curve C (i.e., we have a surjective morphism from Y to C such that the general fibre is smooth and irreducible) such that every fibre satisfies the same vanishing condition. If an irreducible smooth fibre is not affine, then the Kodaira dimension of X is −∞ and the D-dimension of X is 1. We also discuss sufficient conditions from the behavior of fibres or higher direct images to guarantee the global vanishing of Hodge cohomology and the affineness of Y .
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تاریخ انتشار 2005