Threefolds with Vanishing Hodge Cohomology
| dc.creator | Zhang, Jing | |
| dc.date | 2003-12-11 | |
| dc.date.accessioned | 2026-07-07T05:03:49Z | |
| dc.date.available | 2026-07-07T05:03:49Z | |
| dc.description | We consider algebraic manifolds $Y$ of dimension 3 over $\Bbb{C}$ with $H^i(Y, Ω^j_Y)=0$ for all $j\geq 0$ 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 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 $-\infty$ 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 $Y$. | |
| dc.description | 24 pages, accepted by Transactions of AMS | |
| dc.identifier | https://arxiv.org/abs/math/0312239 | |
| dc.identifier | http://arxiv.org/abs/math/0312239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69568 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J30, 14B15, 14C20 | |
| dc.title | Threefolds with Vanishing Hodge Cohomology | |
| dc.type | text |