There Exist Nontrivial Threefolds with Vanishing Hodge Cohomology
| dc.creator | Zhang, Jing | |
| dc.date | 2005-04-07 | |
| dc.date | 2005-10-11 | |
| dc.date.accessioned | 2026-07-07T06:39:44Z | |
| dc.date.available | 2026-07-07T06:39:44Z | |
| dc.description | We analyze the structure of the algebraic manifolds $Y$ of dimension 3 with $H^i(Y, Ω^j_Y)=0$ for all $j\geq 0$, $i>0$ 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 $X-Y$. | |
| dc.description | Revised version. Accepted by Michigan Math. J | |
| dc.identifier | https://arxiv.org/abs/math/0504142 | |
| dc.identifier | http://arxiv.org/abs/math/0504142 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101186 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14B15, 14C20, 14J30, 32Q28 | |
| dc.title | There Exist Nontrivial Threefolds with Vanishing Hodge Cohomology | |
| dc.type | text |