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There Exist Nontrivial Threefolds with Vanishing Hodge Cohomology | | Jing Zhang
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7 Apr 2005 | | Abstract: | We analyze the structure of the algebraic manifolds $Y$ of dimension 3 with $H^i(Y, Omega^j_Y)=0$ for all $jgeq 0$, $i>0$ and $h^0(Y, {mathcal{O}}_Y) > 1$, 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 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 $-infty$ and $D$-dimension 1, where $D$ is the effective boundary divisor with support $X-Y$. | | Source: | arXiv, math.AG/0504142 | | Services: | Forum | Review | PDF | Favorites | |
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