On the $D$-dimension of a certain type of threefolds
| dc.creator | Zhang, Jing | |
| dc.date | 2006-10-28 | |
| dc.date.accessioned | 2026-07-07T07:29:34Z | |
| dc.date.available | 2026-07-07T07:29:34Z | |
| dc.description | Let $Y$ be an algebraic manifold of dimension 3 with $H^i(Y, Ω^j_Y)=0$ for all $j\geq 0$, $i>0$ and $h^0(Y, {\mathcal{O}}_Y) > 1$. Let $X$ be a smooth completion of $Y$ such that the boundary $X-Y$ is the support of an effective divisor $D$ on $X$ with simple normal crossings. We prove that the $D$-dimension of $X$ cannot be 2, i.e., either any two nonconstant regular functions are algebraically dependent or there are three algebraically independent nonconstant regular functions on $Y$. Secondly, if the $D$-dimension of $X$ is greater than 1, then the associated scheme of $Y$ is isomorphic to Spec$Γ(Y, {\mathcal{O}}_Y)$. Furthermore, we prove that an algebraic manifold $Y$ of any dimension $d\geq 1$ is affine if and only if $H^i(Y, Ω^j_Y)=0$ for all $j\geq 0$, $i>0$ and it is regularly separable, i.e., for any two distinct points $y_1$, $y_2$ on $Y$, there is a regular function $f$ on $Y$ such that $f(y_1)\neq f(y_2)$. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610881 | |
| dc.identifier | http://arxiv.org/abs/math/0610881 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118158 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14J30, 32Q28 | |
| dc.title | On the $D$-dimension of a certain type of threefolds | |
| dc.type | text |