There Exist Nontrivial Threefolds with Vanishing Hodge Cohomology
نویسنده
چکیده
We analyse the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application of these theorems, we give the first example of non-affine, non-product threefolds Y with this property by constructing a family of a certain type of open surfaces parametrized by the affine curve C−{0} such that the corresponding smooth completion X has Kodaira dimension −∞ and D-dimension 1, where D is the effective boundary divisor.
منابع مشابه
On the Existence of Nontrivial Threefolds with Vanishing Hodge Cohomology
We analyze the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application, we prove the existence of nonaffine and nonproduct threefolds Y with t...
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